While the accepted minimum for the species is 1 gallon, bigger is definately better; safer heating, stable temp, less frequent water changes, better water quality etc. I personally would not go smaller than 2.5g (inch per gallon rule), with 5g being preferable, and 10g
great, esp. if you want to include some snails or small algae-eating fish. Since you want to heat and filter, 5g+ is the safest; there are heaters for 2.5g, but they can cause the tank to overheat very quickly.
Heating, unless you room temp is steadily at ~ 75, is a must. Bettas prefer temps in the mid/upper 70's to low 80's, with something to the tune of 76-80 being ideal, and 72-84 being "ok" (I think; don't quote me on that. My tanks have been at 76 for so long that I don't worry much about temperature fluctuations any more).
A simple HOB filter would be fine for a 5-10g tank. You may have to put filter sponge or pantyhose around the intake to prevent the betta from getting stuck, and it would be strongly preferable to find something with a gentle output as bettas are not a fan of current - especially the long finned kind, which I assume you are getting if you are buying from a pet store. A plakat could probably handle current like a "normal" finned fish, but they aren't easy to come by unless from a breeder. Sponge and UGF filters are also good for bettas, but I don't think they're very good if you want to do a cycled tank.
Regardless of your tank size, you want to make sure it is well planted. Bettas love to hide, and fish with long fins - esp. ones being kept in a large tank with a filter - need something to rest on so they don't exhaust themselves to death. You can choose to go fake or live, but I suggest only using silk plants if you use fake, as plastic can rip the fins. You may also want a cave; any commercially available cave with soft, rounded edges is safe, and you can DIY your own as well. I know some great advice for this, but it is at a forum potentially viewed as competative to this one, so you'll have to PM me if you want 'em.
Also, if you choose to do a 10g and want other fish, please read the info on compatible species first! Your bettas disposition may demand that he is a lone fish. Other bettas don't mind small, passive, dull-colored fish. Many people use small catfish (blanking on the name; they are small, social, and only get to be a few inches), which bettas generally ignore, but remember you'll want to quarentene them first as many tropical fish are wild caught or from large scale fish farms, both of which are a good source of parasites and disease.
You could also add some invertebrates or ADFs, but I warn that bettas sometimes think snails and shrimp are just a really expensive snack (lol). Snails have a high waste output and destroy most live plants, so keep that in mind.
