As an alternative to a Betta.
You might also want to consider shrimp- there are a number of f/w varieties out there- transparant/red/yellow/green/brown/blue/white/black... etc.
Some of which can be kept together without worry of hybridising into a less desirable colouration.
If you can't find them in your stores- check the classifieds here- people are frequently selling them for $1. Ghost Shrimp are usually 25cents to 33 cents apiece at your local chain pet store- these are usually the only ones you can find in stores without ordering online.
Red Cherry Shrimp can be purchased $1 each on here... Both are very hardy and forgiving- although most people frequently have losses at first.
Personally, as beautiful as Betta can be- little dwarf shrimp are more entertaining to me and you can keep quite a number. I think the rule I read with Cherries is up to 10 per gallon... BUT DON'T buy that many- because they will reproduce on their own. (most species will in an aquarium anyway).
Plenty of people keep Betta in 3g containers and keep them healthy and happy- but I don't think you see the best of a fish unless you give them more room.