Depends what suits you. :) Because you have a snail as well, I would recommend at least a 3 gallon, but preferrably a 5 to help dilute the ammonia produced. :)
Definitely get a heater. Although bettas are hardy and can live at sub-optimum temperatures, it is like a human living in the cold constantly with no way to warm up. It depresses their immune system, so they are more susceptible to illness and find it harder to recover when they do get sick. Warm water also makes them hungrier, more active and more colourful. :) 78-82 is the optimum range.
Again because of the snail, I would consider a filter. If you get a 5 gallon, definitely get a filter so you can cycle the tank (SO much less work). Without a filter, in anything under a 5 gallon, you'd be looking at 1 50% and 1 100% change per week. With a filter in less than 5 gallons, 2 50% would probably suffice. In a cycled 5 gallon, 50% once a week would be fine. :)
Shopping for new tanks and toys is the best fun...I spent about $100 on my rats at the petshop yesterday. *rolls eyes at self*