Howdy! Just got back from Italy myself, and while we took the circumvesuvia from Sorrento TO Naples, we took the ferry back TO Sorrento from Naples. I think your choice is wise, the train is pretty sketchy (and I lived in NYC for over a year).
It cost about $24 one way per person, and they prefer cash although they take cards. As you get into the port you will see a huge building with SATVA on it, don't go that way go right instead. Behind the castle there is a long line of ticket booths. Just look for the one that says Sorrento. Could not be easier. We did not buy in advance, it's a HUGE ferry and the ride is lovely. Took about 40 minutes to cross the bay into Sorrento.
When you arrive in Sorrento follow signs for the lift behind the beaches if you want to get up into town, cost one EURO. Otherwise you can grab a cab or SITA bus in the port. Cabs in Sorrento are a rip off, cost a min of 15 EURO, avoid if you can. Learn the bus system, it's a blast and cheap. You won't want to walk up the stairs with your bags, it's over 100 steps and nearly straight up.
From Naples airport take a taxi to the port, it's pretty reasonable from what I was told. Less than 20 EURO. Not really another option, and they are no where near each other.
We ended up using a private transfer from airport to hotel in Sorrento just for the ease and convenience and I would do it again in a heartbeat, especially after long travel day. Cost was 80 EURO and the hotel arranged it.
Have fun, Sorrento is a joy!
