The Airport Limo is the cheapest and easiest method, especially if you are going to a Tokyo hotel. The Narita Express train should be quicker (to Tokyo, but maybe not your final destination), but maybe a little more expensive (depending on class of ticket). It only stops at Chiba, Tokyo, Shingawa, Yokohama, Ofuna, Shinjuku, Ikebukuro, and Omiya, so if you want to get to Ueno you need to transfer at Tokyo station.

There is also a Airport Narita train that offers more of a "local" service. Cheaper, with a whole lot more stops.