Live plants are a great idea for any aquarium, assuming, like Alex said, you don't have fish that will destroy them. Plants will help remove harmful nitrogen compounds from the water, especially if you have species that will grow quickly and constantly reproduce, like water sprite or hornwort. Those two species in particular are also great because you can just let them float at the surface of the water and forget about them (and they actually grow better this way, as opposed to planting them in the substrate), and if you're keeping skittish or nocturnal fish, they will appreciate the shade that these plants provide.
Another good plant to buy is Anubias. Anubias grow extremely slowly, so they won't absorb as much nitrogen, but they're very hard to kill, so they're nice to have for decorative purposes in a beginner tank. The one thing to remember with Anubias is that you can't bury the rhizome (the horizontal structure that the roots grow out of). The best way to plant them is to tie them to rocks or driftwood with thread; it's actually not even necessary to bury the roots in the substrate.
And if you do want plants that you can actually plant in the substrate, you can always look into the various species of Hygrophila, Cryptocoryne, Ludwigia, Rotala, Vallisneria, Hemianthus, etc. You'll just have to make sure that the specific species you're looking at is recommended for beginners. If you do a Google search like "Hygrophila for beginners," you'll be able to find several suitable species.
The most important thing for you to have success with plants is going to be to avoid letting algae get out of hand. Algae will compete with the plants for resources, and if the conditions aren't right, algae will always win in the end. As long as you make sure your aquarium isn't exposed to natural light (i.e. near a window), you don't leave your lights on for more than 8 hours per day, and you keep an adequate water change schedule, you probably won't have any issues with algae.