When looking for plants, look for low-light plants that can tolerate cool water, are suitable for your water conditions (pH), are tough (axolotls will snap at moving leaves/stems), and can tolerate low light. That eliminates most plants in the aquarium trade ... :happy:
Anubias are tough and low light, and can be mounted on a rock to keep them in place. Marimo moss balls are low light, but once in a while, an axie will damage one. Duck weed is a good floating plant that will cut the light reaching the bottom of the tank, and some keepers love it, but my axies eat it (accidentally, I think).
Pros to plants are that they absorb some of the nitrates (but you still need to do regular water changes). Cons are they are another living thing in the tank, and decaying plant matter (if they die) is another source of ammonia etc.
If you want a bare-bottom tank, then you need plants that can get mounted to something like a rock. (Some plants need their roots in a substrate.)