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.
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.
Not every probiotic needs to be refrigerated, and just because one does doesn't mean it's better than one that doesn't.
There is also widespread misinformation about needing to take prebiotics with probiotics in order for them to be effective. This is false. Probiotics can be effective on their own, and general/random prebiotics may be counterproductive since they will usually feed a wide range of microbes rather than the specific one(s) being targeted. Finding a prebiotic that only feeds the specific targeted bacteria can be difficult.
If a probiotic/microbe isn't making it through the digestive system/juices it likely hasn't evolved to be host/human-native. Not every "probiotic" belongs/thrives in humans.
Take before, or with a meal.
Citations & more info: /r/HumanMicrobiome/wiki/probiotics