The only problem with the Keisei limited expresses is that not all of them go to Nippori, and for a first time visitor, ending up somewhere strange would be awkward. All Skyliners go to Nippori and Ueno, however, and -- let's be honest -- they are more comfortable. This would be the fastest way to Ikebukuro.

In the afternoon, when most international flights arrive, only every other Narita Express train goes to Shinjuku, so that's only once per hour. But BACK to Narita, there are Narita Express trains every half hour in the afternoon.

It is uncommon for these trains to sell out, but on my arrival in Tokyo last time, the Narita Express had sold out. This has happened to me twice in about 30 trips to Japan. I don't think I'd book in advance since if your flight is early or late, you are stuck with your ticket converting automatically to a standing room ticket.