After going over all this with my daughter, and looking at some LFSs today, she's decided on a Betta and likely a couple Mystery Snails. We can get a 50W heater cheap enough and then we'll never have to worry about tank temps. In our journey today we saw a couple larger Fancy Goldfish, which was helpful so she could see how inappropriate they would be in a small tank.
Now I just need to get the 5g tank set up and cycled (should be quick since I have media from my 29g tank to kickstart things), and then we can make one Betta's life a lot better by giving it a proper habitat. Thanks for all the input, everyone!