The antibiotics can play hell with your gut biome. Probiotics can help fix that much more quickly than if you just let it happen on its own (and it will, just fine, for 99.999% of people). I have never bothered with probiotics after antibiotics, nor has my doctor recommended them, but I did do a good course of them after I had c. diff. My doc gave me a cocktail of probiotics and other supplements, because I really did feel wretched and had a hard time getting back to eating normally for weeks.
Not all probiotics are the same. After antibiotics, you need to rebuild lactobacilli (for example, Lactobacillus acidophilus and Lactobacillus GG), bifidobacteria (such as Bifidobacterium bifidus) and some yeasts (Saccharomyces boulardii). The strains you also may want to look for in a supplement are:
L. casei
L. Rhamnosus GG
L. Plantarum 299v
B. subtilis
B. coagulans lactospore
B. clausii
Generally, you want to take something that gives you about 25 million of these buggies/day for 30 days.
In addition, she recommended L-Glutamine, which helps a somewhat torn-up gut rebuild healthy cells.
Probiotics come in powdered forms in capsules (generally shelf stable, but only for a limited time while fresh), or in refrigerated capsules, which are less stable. There's no difference in effectiveness, as long as they are kept correctly, and not expected to work after months and months of sitting around. Even the ones you get that are freeze-dried and shelf-stable should be keep in a cool, dark place.