A 2.5 gallon would work for a betta, shrimp, snails, and possibly an African Dwarf Frog (but I'm not completely sure about that last one). Be sure to heavily plant the tank as well! Good luck with your new tank!
You could do a shrimp only tank! I've always wanted to.
There are many easy Neocardina and Cardina species that are easy to care for and breed like mad if you have enough of them. A couple to look into are Red Cherry Shrimp and Crystal Red Shrimp. There are also other variations like Yellow and Orange Shrimp. Another shrimp to look into is the Ghost Shrimp (though they are a bit harder to breed than the others).
A betta, a betta and shrimp, a betta and snails, or all three are a possibility. Some people say steer clear of keeping bettas with shrimp isn't a possiblilty, but it is! I've had some bettas they never even looked at the shrimp in the tank. All bettas have different personalities.
One thing you could try to test out if the betta is shrimp friendly is to use Ghost Shrimp since they are only around $.88 at the store. If your betta eats/picks on them, not much money is wasted! If he doesn't, then you should be in the clear to add other types of shrimp. Another thing you could to do to steer the betta away from the shrimp is to have a lot of decorations/plants/fake plants in the tank. Most bettas have been stuck in a small enclosure their whole life, so if they were introduced to a tank with lots of places to explore they should be pretty distracted (it also gives places for the shrimp to hide). And one thing I recommend if you do try the betta/shrimp combo is to have the shrimp in the tank first!! Introducing the shrimp after the betta could look like you're just dropping food into the tank.