Welcome to Troipcal Fish Keeping forum. Nice to have you with us.
I'm not much on carpet plants, so I will leave it to those who have them to suggest species. I would just point out that in general, they require somewhat higher light and correspondingly more nutrients than most aquarium plants. This is why I don't have them, but several other members do, and they'll probably be along shortly unless they're on summer vacation as many members are at present.
carpeting "grass" often doesnt need higher light and often depend on light to control their heights. Fast growing carpeting plants are glosso, dwarf hair grass, and dwarf chain sword. However, all three of these need high light to thrive and/or stay at the appropriate height. More moderate growing carpeting plants are HC, and glostigma. Slow carpeting plants are brazilian microsword. As for mosses, the faster ones are the common ones like java moss, christmas moss, etc. The slower ones are the various fissidens. There are many many more options, but these are the basic ones that are the most popular.
forum community dedicated to tropical fish owners and enthusiasts. Come join the discussion about species,breeding, health, behavior, aquariums, adopting, care, classifieds, and more! Open to fish, plants and reptiles living in freshwater or saltwater environments.