Keep up with trimmings, like noted above. Instead of tying the moss down, you could also cover it with a mesh-like material. That way when it grows through, you can lift it up and trim easier.
But as far as plants that you want to add go, it all depends on what you want. Are you wanting all green? maybe some red here and there? long leaves, rounded leaves? You can always start out with some Ludwigia, since that's pretty common and fairly easy to keep up with. Maybe some Anubias or java fern