Going from Tokyo Station to Shinjuku, I would take the orange JR Chuo Kaisoku train. It only stops at Kanda, Ochanomizu and Yotsuya before arriving at Shinjuku station, and therefore be the fastest mode of public transportation.
Keisei Bus also operates a bus service between Narita Airport and Tokyo Station. See
Discount airport bus "Tokyo Shuttle" to operate from July 3, 2012
The current fare is 900 yen from Tokyo Station to Narita Airport, and 1000 yen from Narita Airport to Tokyo Station. The bus stop is a bit farther away though.