Remember that floating plants will affect the amount of light that reaches the bottom of the tank.
You've heard a lot of good advice on here...it's important to keep it simple when you're just starting out.
I wouldn't bother with stem plants yet...anacharis and elodea can get messy in low light. Just try some of the anubias (practically indestructible) or java fern (same). Couldn't possibly get any easier than that.
Also, your betta will like the broad leaves of the anubias for hiding under or maybe even resting on. Anyway, that's my .04, since I posted twice...good luck with whatever you choose!