5 gallons is the best size for a betta. No less than 2-2.5 gallons IMO. You can get second-hand tanks, they're very cheap. I would say a heater is quite essential, colder temperatures lower their immune systems so they're a bit more susceptible to disease. Even lower than that (70F or less, about) they can probably die much more easily.
How much money can you spend? If you don't have a lot of money to spend, then you should wait before getting one. Fish are not exactly cheap little things if you want to really be interested in it.