I agree with Jayce, often pet stores don't tell the proper care of bettas, did you know they can live up to 8 years! But rarely do they live more than a few months due to all the mis information given.
I'd say 5 gallons with a mini heater is good and slow moving filter, but they do great in 10 or 20 gallons with some live plants added (they rest on leaves floating near the surface at night). They can get along with some other tropical fish too that are peaceful and don't nip fins or have long fins. Bettas don't eat plants they are carnivores; so frozen brine shrimp, daphnia, bloodworms, and soft betta pellets are good but if you can find live of those foods even better! Yes they are tropical fish cold water will make them sick quickly.