duckweed is super easy to grow, it's a floater so it has access to all of the co2 in the air and in my experience, doesn't need too much light. It grows SUPER fast and makes it hard to get your hand into the aquarium without looking like a lake monster when you pull it out. But you most certainly can grow it.
With leds, you might want to lean toward low light plants.
Anarchis is really cheap and a good grower as well, but it likes it a little cooler, so I'd keep the betta tank on the lower end of acceptable (76ish) if you decided to keep it.
Anubias Nana This is by far one of my favorite plants for small tanks. It gets to around 6 inches which is perfect for my small betta habitats. It has huge leaves bettas can lie on, and is almost impossible to kill. *knocks on wood*
Java Fern is great too, and you'll have dozens of plants in no time at all.
One of the easiest plants to grow in my experience is guppy grass. I recieved a tiny little bunch (one plant about 3 inches long) and in the span of two months, my 30 tall with a 20watt light is filled with the stuff. I just threw it in as a floater, and it grows toward the subtrate and plants itself. If you plant this, you will be trimming every two days, but it uses up a lot of nutrients, which is good for small tanks.
Both of the mosses you mentioned, should do fine, Java moss in particular is hard to kill, had a bunch turn brown at the bottom of my 48" might-as-well-be-dark monster tank, but I just threw it in my spare plants tank and it came back to life.
Sunshine: a yellow veiltail. Moonshine: a crazy mix of blue, black, purple, and copper deltatail. Clark: a red and blue feathertail. And Jack: my dream betta, a solid white EE plakat.