I have a 20 gallon natural light tank. It has an inert sand substrate. This tank was my first experiment with live plants. I also had a shrimp tank that was natural light right next to it. The plant that has done the best is guppy grass. Shrimp love this stuff and it's much easier to manage than Java Moss. You can grow it thick or thin, float it, tie it, plant it. It's one of my favorite plants because it's so easy to grow, and it's so versatile. Oh yeah, and I never dosed ferts in those tanks. Anubias will do well. Just mind where you place it. I recently started up a 10 gallon tank with a bunch of crypts. I had some let over, so I am experimenting with them in the 20. I have had them for about 3 weeks now, and the crypts in the 20 are doing really well. In fact, that was the only tank I haven't had crypt melt in yet. A carpet plant you might want to try is crypt parva. I would skip the duckweed and use a larger floating plant like red root floater or frogbit. Keep in mind through that your tank is so shallow, that you would need to keep these trimmed. I also put some pennywort in that 20 gallon and it seems to be doing really well. Your betta might like that. You could always use that as your floater too. Vals may be too tall for what you are looking for.
This isn't rocket surgery