Aquatic plants will continue to grow if they are healthy. They are never "mature". Eventually even anubias can need pruning and thinning out. I think what you want is a low light tank, with slow growing plants, so you only need to attend to pruning once a year or so. If that is true, you will want to avoid stem plants, which tend to be very vigorous growers. You will want to avoid vals, which reproduce like rabbits! You will want to keep the light intensity down to around 25-30 PAR at the substrate. Anubias are very subject to algae problems, due to their large leaf surface, non growing mature leaves, and very slow growth, but they would fit your needs if you can avoid the algae. Mosses would also fit your needs, but can also require a lot of thinning out. With mosses and anubias, you could probably get by with as little as 20 PAR at the substrate, further reducing the exposure to algae problems.
Look for a light or lights that will produce about 20 PAR at about 20 inches distance, assuming you will have 2 inches of substrate. That could be Marineland double bright LED lights.