Live plants require certain amounts of the right kind of lighting to grow. If your aaquarium comes with a standard light hood and bulb, you wont be able to grow much. You can upgrade your lighting if you want. If your wallet is thick there arent many plants you cant grow. However, the higher (not price) the lighting, the more effort and money you will usually have to put into it. High light plants tend to grow fast requiring regular trimming and Co2 injection.
A low to medium light setup isnt too pricey. Shouldnt "require" Co2 and shouldnt be too difficult or time consuming to maintain. This is the route I am taking at the moment for my first tank.