If you find this overwhelming, just try the probiotics in the "recommendations" section one at a time, while minimizing fermented food intake. If your main problem is constipation bb536 is getting good results, and there are others listed in the "prospects" section below. If you've tried a variety with poor results perhaps try adding phages.
Since some people are still having trouble, here are the main takeaways:
- The current products are extremely limited and thus many people will get poor results no matter what. Many prebiotics and probiotics can cause various harms. Prebiotics generally seem to soften & bulk stool since they feed bacteria. Avoid supplements with many different ingredients, especially prebiotics, unless you already know that specific prebiotic is beneficial for you.
- There's a big difference between strains (and this term is often misused), and where the probiotic was sourced from. Most of the literature backs a few specific strains for specific conditions. Different types & strains will have different effects . You can't just go for more.
- There's already a recommendation section so why are you still asking for recommendations? Also see the last paragraph of the "Intro" section.
- Any rules that exist are vague, and people have to experiment for themselves due to major person-to-person variation .
- Try the most backed/studied human-sourced probiotics first. Strains have host-specific effects, so you can't expect to get the same results of an animal study .
- Fermented foods are generally quite oversold and can have detrimental effects. They are also not interchangeable with probiotics, except for ones sourced from fermented foods, like Garden Of Life products.
- Fermented foods and multi-strain probiotics may hinder, rather than help, recovery after antibiotics . Though some probiotics are certainly proven to help prevent antibiotic associated diarrhea .
- Take before, or with a meal. Citations & more info: /s/HumanMicrobiome/wiki/probiotics
What's effective for someone is going to vary between person to person because it depends on the current microbes that are in each person's gut. You sort of have to try a wide variety of products and see which one works for you. Though the following information should help narrow it down. People who have taken certain antibiotics or a lot of antibiotics will likely benefit from the same probiotics (probably human-derived ones, since that's what the abx kills off).
The current products on the market are extremely limited in comparison to the vast amount of microbes in a healthy human gut, so one should not expect to find a probiotic that completely cures them. Up until early 2016 we were only able to culture around 1% of gut microbes [1, 2].
Unfortunately, less than 1% of Amazon reviewers actually say whether a product helped with "constipation" or "diarrhea", which makes the reviews completely useless. Please be specific when you share your experiences here and elsewhere.
One of the most important factors seems to be whether a probiotic is human-derived or food-derived. Human-derived strains seem to have the widest range of benefits. Most human-derived probiotics are native strains that would be the most likely to perform native functions, and colonize the gut (but still typically do not colonize). Whereas most food-derived strains have very different effects/mode of action, and are transient.
Additionally, most human-derived strains seem to have anti-diarrhea effects, whereas food-derived strains seem to mostly be anti-constipation. I started a list below (stickied comment) of products and the sources of their strains.
These show what the most science-backed strains/products are:
https://sci-hub.tw/https://doi.org/10.1097/MCG.0000000000000420 - 2015 one from Yale & Harvard
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3424311/#S8title - Older one from 2012: "A GI's guide to probiotics"
Strain identifiers (the numbers/letters after the genus and species) are probably the most important factor when looking for a probiotic. I had no positive results with probiotics until I figured this out. I originally read that maximizing number of strains & CFU counts were the most important things, and I got no results (besides stool softening) with that approach. Many probiotics don't even list the strain, and often contain many inaccuracies.
A major downside is that you can't find a single product with a bunch of different "good" strains. So purchasing separate products for single strains gets expensive. I don't see this being resolved until a "synthetic FMT" product is available.
Spore formers, soil-based bacteria:
Just a warning that some spore-forming bacteria like these soil-based ones in Prescript-Assist, are very risky since they can take over the gut. I've had extremely severe detrimental affects (additional citations included) from this one, and haven't yet been able to get rid of it.
Additional citations against SBOs in my probiotic archive: /s/HumanMicrobiome/wiki/probiotics
There's an "appeal to nature fallacy" that is common in health topics. IE: we used to be naturally exposed to these things therefore they must be good for us. This fallacy is being applied to soil bacteria.
Environmentally sourced microbes are very different from host-derived 
Currently the science shows the beneficial microbes are the ones given to us in the womb, during birth, and from breast feeding & early healthy diet. It's very probable that these microbes prevent other commensal microbes from doing us harm. So there is risk with just introducing random microbes that are "typically found in the gut".
Two fungal species cooperate to synthesize an antibiotic that neither produces when grown alone. The antibiotic kills MRSA, as well as the bacteria that cause anthrax and strep throat. (2017): https://www.acsh.org/news/2017/05/01/two-fungal-species-cooperate-synthesize-antibiotic-11215
We found that the probiotic therapeutic effect was varied across individual mouse even with the same genetic background and consuming the same type of food. The different probiotic efficacy was highly correlated with different microbiome features in each mouse (2018): https://www.biorxiv.org/content/early/2018/06/06/340331
An example of the variability: I found some probiotics that have really good, powerful benefits for me. Then I added Prescript-Assist and it almost completely negated the affects I was seeing from the others. Another example is that brewer's yeast seems to only have beneficial affects for me when I take it along with unheated Monterrey Jack cheese (and same for the cheese). And others may have short term benefits (because they seem to work like a bulldozer/disrupter) but detriments the longer you take them.
Another example is that if I'm on a milk-ONLY diet and add some raw milk it will cause diarrhea. But adding 1/2cup raw oats per day to the milk-only diet prevents the raw-milk-induced diarrhea.
And to get the strongest benefits from the probiotic combo below I had to stick with a low fat, low protein, vegan diet consisting of primarily fruits, sweet potatoes, and white rice.
And after an FMT or two, Align makes the soil-bac-symptoms worse, but the Lactobacillus probiotics are still helpful. My guess is that it has something to do with niches being filled or not , and maybe the corresponding phages play a role.
Saccharomyces boulardii is supported in the literature to have anti-diarrheal effects. Jarrow's s.boulardii definitely does this for me. But other people have reported other brands/strains of s.boulardii to have the opposite effect on them.
And while Jarrow's s.boulardii helps massively for me with fatigue & diarrhea, someone with mast cell activation syndrome & IBS-C said the MOS in it seems to be problematic for them, and this s.boulardii product without MOS is better for them.
Synbiotics: Taking probiotics with the same meal as synergistic prebiotics can boost their power and change the effect the prebiotics would otherwise have.
With this in mind, I have a history of a lot of different antibiotics (along with CFS, IBS-D and others). By far the largest benefits I've seen (boosts to energy, brain function, strength, skin, sleep & dreams, sex drive, happiness, anti-diarrheal, etc.) have been from s.boulardii (Jarrow's brand with MOS), which is the only fungal product on the market that I know of. Many of the benefits seemed to come from/with improvements to intestinal permeability, and possibly immune function .
I have also benefited largely from this phage product. Make sure to get one that has no other additives or ingredients. I recommend taking phages separately from bacterial probiotics because they seem to change the impacts of other products. I take them alone with juice/water and s.boulardii, first thing in the morning. And they seem to have good anti-diarrheal/antibacterial effects. Bacteriophages as prebiotics: /r/HumanMicrobiome/comments/6n76p9//dk7a2k4/
In the past I have benefited from Reuteri Pearls, plus culturelle, plus align, which seemed to be more effective when taken all together.
I have seen benefits from Bimuno when other prebiotics were only harming me. But I do not take it at the moment. Bimuno is GOS (galacto-oligosaccharide). Oligosaccharides are long-chain sugars (fiber) that feed bacteria, usually bifido.
Reuteri and b.infantis are species found in breast milk. Lactobacillus GG is the most studied probiotic strain. Align & Culturelle are the two most backed strains in the literature, and both are also sourced from humans. That particular Reuteri product seemed to, at one point, benefit me significantly more than a very similar product from the same company with a different strain of L.reuteri.
Culturelle + mushrooms are synergistic so I'd take them in the same meal.
Align & Bimuno are synergistic so you could take them together in another meal.
Jarrow's s.boulardii is more powerful/beneficial for me than Florastor. It's also cheaper which is nice. Some people have reported issues with Florastor.
I would recommend introducing each product one at a time (for a few days each) so you can see what effect it has.
As of January 2018 it seems that pretty much every current bacterial probiotic harms me. So I only take Jarrow's s.boulardii & phages. Actually, looks like Culturelle is good, it was just the inulin in some of them that was harmful.
B. longum BB536: http://maypro.com/products/morinaga-bb536 - http://www.morinu.com/en/b-longumbb536/ - http://www.humanclinicals.org/#/bb536-1/ (human-sourced strain, but seems to be mostly anti-constipation). Multiple reports of it curing IBS-C.
BioGaia Gastrus has one or more human-sourced strains, but also has some unnecessary additives that might cause problems for some people. Though certain Culturelle formulas also have problematic additives, and even Bimuno. It didn't do much for me.
Lactobacillus gasseri CP2305: A human-sourced strain that colonizes 40% of recipients, but seems to only be available in one Japanese product. This company says free shipping from Tokyo.
Just Thrive's Bacillus spores may help with CFS, IBS-D, and intestinal permeability: http://thriveprobiotic.com/groundbreaking-study-healing-leaky-gut-strains-used-just-thrive-probiotic/
Bacillus Subtillis http://deerlandenzymes.com/de111/#section2
Bacillus Coagulans is a spore-forming, L-lactic acid producing bacteria that looks promising for IBS-D, and more. Didn't do that much for me, but the ProDURA strain does seem to help with bile-caused dysbiosis when taken in the same meal as fat/protein foods [1, 2].
AOR Probiotic 3: Has 3 species which are uncommon in other products. On their "label info" tab they say 2 of them are human-sourced: http://www.aor.ca/en/product/PROBIOTIC-3 - https://www.amazon.com/dp/B0082DDQH6 | Discussion: https://archive.is/c04T7 | Warning about one of the species: https://www.amazon.com/review/R2XMYCGKIQ7U1I | Reviews = people praising it due to things they've read about it, without giving details of its affects on them personally.
Super Human Probiotics - claims to have 15 human-sourced strains + 4 food sourced: https://elementalwizdom.com/products/super-human-probiotics - The testimonials/reviews don't look promising.
Bifidobacterium lactis Bb-12: (available in Yo-Plus yogurt, LiveActive cheese) http://www.webmd.com/diet/features/answers-to-your-questions-about-probiotics#1 - https://www.amazon.com/Trubiotics-Supplements-Count-Blister-Pack/dp/B007RA4J08
L. plantarum 299v: https://www.amazon.com/dp/B00O4BPX9O Produces both D & L lactic acid: https://en.wikipedia.org/wiki/Lactobacillus_plantarum - Jarrow's contains potato starch, and reviewers are saying it worsens IBS-D, may help with IBS-C: https://www.amazon.com/Jarrow-Formulas-Organisms-Intestinal-Discomfort/product-reviews/B008OYII4E/ref=cm_cr_arp_d_viewopt_sr?ie=UTF8&filterByStar=two_star&reviewerType=all_reviews&pageNumber=1#reviews-filter-bar
Miyarisan (Clostridium butyricum): https://cfsremission.com/2015/10/19/miyarisan-clostridium-butyricum-revisited/ - https://www.amazon.com/630-Tablets-Miyarisan/dp/B000FQUNB0 - claimed to be helpful for CFS & IBS-D. But someone reported it has similar effects to fermented foods. Also reported it increases BM frequency a lot, so maybe better for IBS-C (one report of same detriments, like irritability, without improvement for IBS-C). I tried it and had the same result. Made me poop more and increased fatigue.
Mutaflor E.Coli Nissle 1917: http://www.probiotics-help.com/mutaflor.html - https://archive.is/jrie0 - the box says it's for chronic constipation. It definitely softened my BMs.
Lactobacillus fermentum ME-3, glutathione-producing bacteria: http://www.essentialformulas.com/efi.cgim?template=discovery_of_me-3 - http://drohhiraprobiotics.com/lactobacillus-fermentum-me-3-summary-of-human-clinical-trials/ - I can't find a product with this strain that does not also have a bunch of extra & unnecessary ingredients.
Epicor - a dried fermentate produced from Saccharomyces cerevisiae - increased red blood cells, other benefits to immune system like colds & allergies.
This is one I haven't tried yet but looks extremely promising (EDIT: nope, another let down. No positive benefits for me. Doesn't seem to do much more than soften stool.) due to the fact that it lists the strain identifiers for every single one, and it uses the strain of L.Reuteri that I've found to be the most effective. This tells me this company knows what they're doing, rather than just being another fish in the sea trying to make money.
High CFU counts, multi-strain probiotics, home ferments like sauerkraut, yogurt, and kefir:
This is the "anti-constipation" or "disruptor/bulldozer" category. The primary mode of "anti-constipation" effects is increasing stool frequency and softness. This can be accompanied with other unwanted side effects though, such as bloating & gas. So these are not necessarily a "cure for constipation".
Similar to the soil bacteria warning, I have not only found these to typically be harmful to myself, but I've seen a number of reports of people taking these multi-strain, high CFU count products and reporting that it caused them SIBO, fatigue, and other detrimental side effects. However, just like with the soil bacteria products, some people will benefit from these and it's not completely known who or why. See the (incomplete) "harmful impacts" section here: /s/HumanMicrobiome/wiki/probiotics
Currently I believe that products (& fermented foods) have this affect due to the strains they contain (typically food-derived strains). And it just so happens that most multi-strain products use these kinds of strains since they're cheaper and not patented. I think most/all human-derived strains are patented, thus you'll only find them in one product.
The more different strains & species, and ingredients (such as prebiotics), one product has, the more likely it is for them to confound or contradict each other. This is one major flaw of the current (8/20/2017) Labdoor rankings. Just because a product with 15 strains has one strain that is backed by science doesn't make that an appropriate product to obtain that strain from.
The benefits of fermented foods are typically WAY oversold by health advocates. They do have some benefits but they are not the right strains that live natively in the human gut . Their primary mode of action is producing compounds like hydrogen peroxide, acids, & alcohol that suppress other microbes  (thus a beneficial affect on pathogens). But they will not colonize the gut, or perform the necessary roles of native strains. Remember that fermenting cabbage (sauerkraut) is done to preserve it. Fermented foods are GRAS (Generally Recognized as Safe) because only a few specific microbes are able to survive in that environment (and those specific microbes are generally not harmful to humans). An environment that is very different from the human gut.
This environment created by the microbial metabolites, decreases the diversity of the end product (from the whole food beginning to the fermented food end) . Gut microbiome diversity is generally considered good.
The primary evidence I've seen for fermented foods is for certain yogurts being beneficial for vaginal health .
While kombucha is often hyped as a “super-food,” only antioxidant and antimicrobial properties toward foodborne pathogens are well established; and it is unknown if these properties incur beneficial impact, even in vitro or in animal models. To conclude, plant-based fermented foods and drinks are usually safe products; few negative reports can be found, but more research, especially human dietary intervention studies, are warranted to substantiate any health claim. (2019): https://doi.org/10.1016/bs.afnr.2018.09.001
Bacteriophages may be an underappreciated component of fermented foods .
Another thing to keep in mind is that more of a good thing is not always better. I've experienced it myself, and seen reports from others having the same experience. High CFU counts and muti-strain products (especially of the wrong strain) may be too strong and disrupt your microbiome too much. More than a pea-sized amount of homemade sauerkraut is too much for me. And with certain probiotics some people resort to breaking/opening each pill and taking about 1/8th the amount.
One of the signs that I'm basing this off is that high CFU/multi-strain probiotics, and probiotic foods like kefir and sauerkraut all have the similar effect (for me) of acting like a stool softener, and causing the stool to contain much more undigested food (much like certain antibiotics like flagyl). Whereas the specific strains that I mentioned previously did the opposite. I've also read many reports of this same phenomenon in other people. Many prebiotics have similar impacts on me, and there is support for this in the literature .
They (multi-strain probiotics & fermented foods) also suppress the soil bacteria as long as I continue to take them. Unfortunately they also increase my fatigue (CFS).
Moderate to high strain diversity, possibly along with high CFU counts, is likely more beneficial to people who need to clear one or more invaders  , and/or have constipation. Whereas specific strains (like align, culturelle, s.boulardii) are likely more beneficial to people who are missing good bacteria (IE: after taking antibiotics), and/or have diarrhea. Though there are numerous single strain products that worsen diarrhea symptoms.
After the soil bacteria and an FMT, one of the human-sourced strains that used to help me (Align) now behaves similar to "disruptors" (as does reuteri pearls) as well so... ¯\_(?)_/¯
May 2018: I read that nutritional yeast is made by growing the yeast on molasses. So I tried that with Jarrow's s.boulardii, both overnight at room temp and fridge temp. Both worked. But even though Jarrow's s.boulardii benefits me greatly when taking in capsule, fermenting it seemed to have the same detrimental effects as other fermented foods for me. I think this has to do with the metabolites (alcohol, acids, etc.) produced during the ferment. I'm guessing that the gut environment brings about different effects. IE: the beneficial effects might be from it displacing or out competing other microbes in the gut, without producing the same metabolites, at least in the amounts created when given pure sugar in vitro.
Some additional citations/info:
I'd recommend the book "The Art of Fermentation" to learn about fermented foods.
A good quote from another book:
In his book “I Contain Multitudes,” Ed Yong, a writer for The Atlantic, argues that, contrary to their reputation as champions of microbe health, probiotic products found in supermarkets - such as yogurt and kefir - do minimal good because they contain bacteria that are transient and chosen not because of their importance to humans but because they’re good travelers and easy to grow.
Study showing higher doses of Align were worse due to the organism's tendency to "coagulate" into a firm glue-like mass in higher CFU doses: https://www.ncbi.nlm.nih.gov/pubmed/16863564
Each animal host seems to have a host-specific strain of L. reuteri, e.g. a rat strain for rats, a pig strain for pigs, etc.: https://en.wikipedia.org/wiki/Lactobacillus_reuteri#Prevalence | Each animal species hosts a unique microbial community: https://news.vanderbilt.edu/2016/11/28/each-animal-species-hosts-a-unique-microbial-community-and-benefits-from-it
Benefits/importance of specific strains (and more): , , , , , , , , , , 
The recommendations for neonates are essentially the same as adults: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3163616/ - also confirms the importance of specific strains & human-sourced strains.
Attempting to extend/boost probiotics with home ferments part 1: https://archive.is/Y6Ku3. Part 2: https://archive.is/goMOR (tldr: failed). More info.
The microbiome is a developing area. New discoveries are constant. The above information will change with time, and I'll make regular updates.