If you see pennywort, nab it. It's a floating plant that is a nitrate sink and bettas love to rest in it. Hardy, easy to grow in any lighting.
Otherwise, java fern, anubias, cryptocoryne wendtii, and water wisteria are all pretty fail safe. I didn't enjoy my hornwort, it shed needles everywhere and was a mess. If you go with the crypts, you'll want to add some root tabs to your gravel since they feed from the roots. The rest will be happy with the liquid ferts.
Also, if your LFS has java moss, tie it down to some decorations or stones for an easy, lush look. Just trim as it tries to take over the tank. I tie mine to flat rocks across the front and take them out to trim when they get too tall. It gives me a pretty 'lawn'.
betta splendens (domestic) | betta imbellis | betta falx