Absolutely forget the travel agent on this item. You are quite capable of handling this yourself. Frank and Tim are correct. Plus, trains from Rome to Naples will most likely require seat reservations. If you're plane is late, you have to go through the hassle of getting your tickets changed if you can't get there in time. If your plane is really late and you get to the train more than 3 hours after departure, you ticket is no good. I'm betting that your travel agent 1) doesn't know about the 3hr. rule after departure or 2) won't guarantee your timely arrival.
Follow Tim's advice. The Leonardo express is a non-stop train between the airport and the Rome Termini train station. It leaves twice an hour throughout the day. Also, as Tim recommends, buy your tickets from Rome to Naples at the airport train station. Again, don't fear missing the train. There are over 40 trains a day between Rome and Naples. It's nothing like you've ever seen in the U.S. In Italy, you're not late for a train, you're just early for the next one. Just be sure when making buying the tickets from Rome to Naples at the FCO train station that you 1) note the time that the next Leonardo express departs and 2) book your tickets from Rome to Naples for about 1 hr. from that time. The Leonardo takes about 22 minutes to get to the Rome termini train station.
When you get to the Naples Centrale train station, you go down to the lower level and buy a ticket on the private Circumvesuviana train to Sorrento. Very easy and very cheap. Again, frequent trains. Note that your travel agent can't buy a Circumvesuviana ticket from the U.S.
Just take your time getting there. You'll enjoy the whole experience.
