First, welcome to this wonderful hobby. And second, welcome to Tropical Fish Keeping forum.
Third, to your question. "Carpet" plants are usually the most difficult to maintain because they need good light (= brighter or more intensity light) and good nutrients which can often mean adding CO2. To keep things simple, with the light you have and relying on nutrients from the fish food, tap water, and perhaps adding a liquid once a week, there are several suitable plants.
Before naming them, the names below will shade, meaning the species are in our profiles so you can click the shaded name to see the profile in fo with photos.
Pygmy chain sword is ideal. Corkscrew Vallisneria might do well, depending upon your water hardness and light. Anubias and Java Fern are easy; these both attach to objects like rock or wood, as explained in the profiles, as does Java Moss. I would stay away from most stem plants because they need higher light and nutrients, being fast growers. Floating plants are always beneficial for the fish, and easy plants for us. Water Sprite is my favourite, but here the stem plant Brazilian Pennywort also works well. Dwarf Water Lettuce is rarer to find.
We should consider your tank light. I assume it is incandescent (screw-in bulb), with one bulb? The best bulb for this would be a CFL (compact fluorescent), in 10 watts, and a daylight having a rating of 6500K. GE, Sylvania and Phillips all make these, you can get them for a couple dollars in hardware-type stores (not fish stores).
A good liquid fertilizer will help, and there are two that I recommend. Seachem makes Flourish Comprehensive Supplement, and Brightwell Aquatics' make FlorinMulti. Whichever, make sure it is the one I name, as they make several products under the "Flourish" and "Florin" names. A small (the smallest) bottle will do you, as you will only use about 1/4 of a teaspoon once a week.