filters aren't necessary, unless you want to cycle. However, if you have a 2.5 gallon (it's size is alright), you can't really cycle a stable cycle. You would just have to do two 50% and one 100% water changes a week.
If you want a larger set up that requires slightly less work....I know petsmart might still be selling an empty 10 gallon for all of 12 dollars, and one aqueon pro heater 50 watts would be 20 something dollars. A filter from walmart would be all of 10 or so dollars as well, and then all you'd have to do is divide that tank between the other two bettas, and they'd be happy as could be. You could do a fish in cycle (50% water changes a week), so long as you don't remove the filter media (you could just stuff the filter full of sponge filter media and clean them in old tank water once a month during one of your water changes).
I feel so bad for those fish. That is animal cruelty right there..... I wish I could explain what that teacher put those bettas through.