Bettas need filtration. Though they breathe air, reducing the need for aeration, they still require benefit of the nitrogen cycle, which turns the ammonia they produce into much less harmless nitrate. Plants, as you seem to know, do this as well, but only in the very best environment would they actually do well enough (the right plants, the right lighting, the right conditions) to consume all the ammonia produced. Buy a little sponge fiilter, cycle your tank correctly, and you'll find life to be much easier and the fish will enjoy a longer, better life. The filter moves the water through media full of beneficial bacteria, thereby allowing that bacteria to "eat" the ammonia, converting it to nitrite, and then other bacteria to convert that nitrite into nitrate. It's hard to achieve this without forced flow through biological media. Here's a link on FW cycling, just in case:
http://www.wetwebmedia.com/FWSubWebIndex/fwestcycling.htm
This is the way to go if you want to enjoy this tank -- what most of us are after!
Edit: And don't forget the heater -- set it at about 78 Fahrenheit and you'll be good. I'm not familiar with the Pleco, but plecos in general produce a lot of waste, and would further necessitate the filter. Be sure and research its maximum size and nutritional needs to insure it is a good fit for the system and is getting what it needs in order to survive and be healthy.