So buy a light. The clip on arcadia arc pod is pretty good if you don't have a hood. If you do have one though, get a light starter and a basic flourescent tube. What sort of tank set up is it? A picture would be helpful to see how you could attatch a light. A desk lamp with an energy saver bulb is better than nothing if budget is an issue.
If you allow sunlight to hit the tank for hours on end you'll start to get algae problems and green water eventually.
Basic "low" light plants would be java moss, Java fern, moss balls and elodia.
If natural light is your absolute last resort then Elodia is the best choice for something tall growing. It grows fine in natural daylight but you will need to keep it trimmed by pinching/cutting it off about 3 CM or so beneath the surface once it touches the top. Moss balls should also be fine.
You will need more than just one or two plants really. Bettas like lots of vegetation to swim through and rest on. So a few bunches of elodia, 2 or 3 mossballs and your java moss and you should do well enough with those.
