you can work it out so both the plant and fish are healthy. Changing and conditioning the water very frequently, making sure there is the most water surface to air contact as possible, feeding the betta betta food, ideally being on top of testing the water. American breeders use on gallon containers, so it seems to suggest to me this is an appropriate size, though the bigger the better.
You don't want a plant that is going to block the top off from air, since they breath it from the surface. dangling ivy or rhodedendron off the edge would be cool. cut back the roots if they get too much. The lilly tends to cut off the air supply...or at least cuts it off more than other options. and the roots go balistic.
banana plants are great, but I have mine in a 30 gallon and their stems are up to a foot/ foot and a half long. I think they also like substrate to root in. my betta loves to perch in a wisteria plant (also low light requirements, like the banana), but again, make sure there is substrate.