I have kept bettas for several years and just to confuse the issue, I will say that I have kept them in larger tanks and smaller ones, with filters and without, with heaters and without.
To clarify:
I keep some bettas in two gallon tanks without filters and without heaters. These fish are in my bathroom, which is warm. I have found that as long as the temperature stays in the 70's, my bettas do great. The temperature in the bathroom is usually around 72 f. Actually, I have found these bettas to be longer lived than the ones I have in heated tanks kept around 78 f. I have had occasions when there has been power outages, and the temperature in the bettas tanks has dropped to 68 f. for short periods, and this hasn't harmed them.
The larger tanks are 5 gallon and 10 gallon and they are heated. They are glass tanks and I have 25 watt heaters in the 5 gallon and 50 watt heaters in the 10 gallon tanks. The little 2 gallon tanks are acrylic tanks and unheated. As tinkerbelll has said, I wouldn't go lower than a 2 gallon tank for a permanent home for a betta.
I don't have filters on my little two gallon tanks. I do 100% water changes on these tanks once per week. I rinse off the ornaments and I fill the tank with tap water that has sat out for at least 24 hours. That way any C02 has dissipated (so the ph will be the same) and the water will be room temperature (the same as the 2 gallon tank). I use Prime as a water conditioner.
With the 5 and 10 gallons tanks, I have Aquaclear filters with sponges in them. I use a piece of filter floss over the outflow of the tank to reduce the current. With these tanks, I generally do a 30% water change every 10-14 days or so. I have river rocks on the bottom of the tank, so I siphon any mulm off the bottom when I do my water changes. If I have 2 bettas in a divided 5 gallon tank, I would do water changes more frequently, then if I have 1 betta in a 10 gallon tank.
I would have a light with them. It makes there colours show up so nicely and I think they are a little more active when they have a light, especially if the room they are in is dark (as ours can be during winter).
My tap water has a ph of 7.8 - 8 and is hard and I have had no problem with my bettas adjusting to it. Use a good water conditioner, such as Prime or Amquel +.
I hope all of this helps. It is just my experience in betta keeping and there are lots of ways to keep bettas

They are fairly versatile. If you have any questions, please do not hesitate to ask.