Betta's will do with out heat but I have found that if you can keep it around the 76-78F mark they are allot more active.....
They do like having a filter on there tanks but will live in a bowl..
I personally like to have my Betta's in a 3-5 gal tank with a filter and heart....
In fact i have a heavily planted 36 gal tank with 3 girls and one boy in there and everyone is good. since they have hiding spots and there is allot of room for them....
But I wont suggest that for a starting point...I would get a Eclipse 5 gal tank that comes with a filter on it and then a heater