For awhile I had my Betta in a 5 gal hex. It was a great environment. The filter didn't bother him too much. (though he couldn't build a bubblenest) It provided plenty of room for him to exercise, and since it is a taller tank that it is wide or long it didn't take up a lot of surface space. It worked out great.
I am currently working on making a 10 gal tank to be an "ideal aquarium" for the Betta. Whatever you can afford just remember that bigger is generally better. A larger tank has more wiggle room before changes become a big deal. For example it takes a larger tank longer to cool down than a small tank. So the larger tank would provide less of a temperature shock on the fish.
If you don't want to go for a 10 gal, I would try for something close to a 5 gal.