Fast train is a piece of cake, as others have stated probably better than having to worry about a connecting flight.

If you are staying in Sorrento, you can get off the train in Naples and they will transfer you to the boat to Sorrento, just make sure your ticket goes all the way through. The train from Naples to Sorrento is nasty and stops about 20 times so do not do that. Taking the boat across to Sorrento is a great way to start your adventure, it is quite beautiful. When you come off the train there will be someone holding a sign and once they gather everyone for Sorrento they walk you out to a bus for the short (maybe) ride to the docks. As someone else stated, watch out for pickpockets (this is true in all of Italy actually).

Naples is a through point only, do not spend any time there.

I second the notion on Hilton Sorrento Palace if you have any Hilton Points (you will need a lot!). My only complaint with the hotel is they close the pool too early. But it is a good location, easily walkable to everything and to the bus that goes to Amalfi. Definitely also spend a day on Capri.

Enjoy!