A single betta would be thrilled with a five gallon, I think. I've also heard that a dwarf puffer can be in a 5 gallon, but please don't quote me on that, because I don't know for sure if that's right. It might be worth looking into, though, especially if you don't want to go the betta route.
hmmm My wife dont like betas and I am just setting this up for my 3 year old in her room. Maybe I will go with five neons is there a female to male ratio I should follow.
I don't reccomend fish tanks for little kids. in fact, I wouldn't recommend any pet other than a cat or dog for a child that young. I don't think at that age they are able to understand that fish can't be touched, ect.
Oh, definately don't get a dwarf puffer for a three year old then. Neons sound like a great idea for a little girl, at least to me. I had a goldfish when I was four years old, but they can be really difficult to deal with. Neons sound great, but I don't know anything about them so I can't offer any more advice.