I have heard such horror stories about the Naples train station that I don't want to take a train.
I have been checking and if I hire a car and driver the cost is from $450 - 700 for the 3 hour ride. In addition a tip might be expected. I really don't want to pay that much.
I could fly Naples to Rome for $200 and add about $100 for transportation to the airport and a few dollars for hotel shuttle to Rome hotel.
I could drive but many say that driving in Italy is undesirable. I read the worst part is getting out of Sorrento. I can rent a car for under $100 and add gas and tolls which will add cost. If I did this I could stop in Pompeii on way.