Water wisteria makes a good plant for new tanks. It doesn't need much in the way of care, and seems to do well in anything from low/high light. Its also Asian, so it fits well with bettas. :) Java fern tied to driftwood is a nice way to go as well. As far as cycling goes, I honestly just use the bettas to cycle new tanks - I've never had a problem with it.
A 10G with just one Betta in it and live plants..don't bother cycling it IMOHO.Just get a liquid water testing kit and keep an eye on the parameters.
Welcome to the forum and good luck with your new fishie friend!