Sorry to post so many questions about, really, a 2-day side trip! We fly into Naples airport on one day, want to get down to Sorrento for 2 nights, then get to Rome by train (via Naples). (I've posted a question elsewhere on how best to use our time with really only one full day in Sorrento). So... airport to ferry, or airport to train station: walkable (with small/med rolling luggage)? What are the exact names of the ferry dock and train station? I see multiple named stations for trains... even ferries... in Naples.
Take a bus from the airport arrivals area to Piazza Garibaldi which is right by the Napoli Centrale train station. Go to the lower level of the station and take a Circumvesuviana commuter train to Sorrento.
Take the Circumvesuviana from Sorrento to Napoli Centrale. Go to the upper level of the station and take a Trenitalia train to Roma.