Betta's are tropical fish. And like all tropical fish, they like clean, warm water. The water should be 76 - 80 degrees. If you don't know what the "nitrogen cycle" is, read the FIRST page of the following link, the second 2 pages are not very accurate:
Personally, I do think you need a filter for any fish, the only difference between a betta and most other fish, is that it can get some oxygen from the surface. Betta's don't like a lot of flow though, so a small filter would be best. Here is a list of some low light plants. What kind of light do you plant of having?