free,
While the Circumvesuviana will get you from Sorrento to Naples, you'd probably be more comfortable on the Campania Express - https://www.sorrentoinsider.com/en/campania-express-train-schedule . If you use the Circumvesuviana, watch your luggage carefully so that it doesn't "disappear".
With either train you'll arrive at the Garibaldi station, which is downstairs from Napoli Centrale. Walk up to Centrale and connect with either the Freccia or Italo high speed trains for your trip to Rome.
There are no reserved seats for the trains from Sorrento to Naples. However the high speed trains have compulsory reservations which are specific to train, date and departure time. You can save money with advance purchase (non refundable) tickets for the high speed trains, but you must be willing to commit to using a specific train. If you're not concerned about the money, just buy tickets for the high speed trains on the day of travel.