Transportation from Naples train station to Sorrento

That is a long ways to go on the first day. You need the train to Termini and then the train to Naples. And finally another train to Sorrento since you are already in the train station. Unless you are burdened with a lot of luggage, I would continue with the train to Sorrento. The local train has a reputation but it will be middle afternoon so you will be fine. Just go to the local level of the Naples train station, turn left and follow the signs to the Circunvesuviana - buy a ticket at the ticket booth. It is probably a hundred yards walk and about another hour on the train. Then find a cab after you arrive in Sorrento. Another alternative that probably be just as quick is to fly to Naples. I think, someone else will have to confirm it since I have no direct experience, there is a bus to Sorrento from the Naples airport.

What Frank said is correct.
Regarding flying to Naples from the U.S. The options may not be too many as Naples is mostly served by low cost European airlines. Lufthansa and maybe Air France may be an option, but if you land in Rome the train is the only way unless you are willing to fork out €250-300 for a private car ride. Alitalia flies to NAP from FCO but with only 3 flights daily.

Curreri Viaggi now has pick up at Napoli Centrale and the Port. Cost is 10 euro.

Are you suggesting that the fare from the train station to Sorrento is only 10 Euro? Given the distance that sounds almost too good to be true. Almost cheaper than the train.

i have already purchased my plane ticket to FCO so that can't be changed and prefer to take the train to Naples rather than another plane. I am really just concerned about the safety of the train to Sorrento from Naples. I am happy to pay for a taxi but don't know which taxis might be reliable and not out to gouge me!

The advice to take the Curreri bus is probably best in terms of cost, but if the taxi fare doesn't matter, just go out the front of the train station (Napoli Centrale) and look for the taxi line. Do NOT succumb to the people who may approach you to take a "taxi" that is unregulated and may be surprisingly expensive (regardless of what price you agree on beforehand); these are pirate cabs. If you think you may be jetlagged, you don't want that hassle.

So, bus or regular taxi.

Posie 54, if the Curreri bus now stops at the Napoli Centrale train station and can take you to Sorrento for 10 euros, that's an easy and inexpensive alternative. However you would be tied to the bus schedule and would still need to get from the Sorrento bus stop, probably near the train station, but I'm not sure, to your lodging, either by taxi or by walking. A taxi or car service should charge around 100 euros to take you from Napoli to Sorrento. Drivers should have a written card of regulated fares in their car, and you can ask to see it. Make sure to confirm the fare before getting into the car. Of course you would get a taxi right after arriving by train, and it would be able to take you right to the door of your lodging, with the driver loading and unloading your bags. If you can afford that expense, it would eliminate a lot of the effort and hassle at the end of a very long day of travel.

Frank, yep, only 10 euro but from the airport ONLY: it doesn't service Centrale.

http://www.curreriviaggi.it/eng/autolinee.html

That's a pretty good deal.

I know that the Circunvesuviana has a reputation but don't think it is any worse than the metro in Rome. We have been on it several times, mid day, with no problems. And the train was not crowded so I think you can easily take the train to Sorrento without any problems unless you have a lot of luggage. Then it is the luggage and not the train that is the problem.

I'd agree, Frank: I know a lot of people here don't like the Circumvesuviana but it really didn't bother us.
But a cab to the airport to catch the Curreri bus might be an economical option too - if economy is a priority.

On the company link that Karen provided, I only find the more expensive private shuttle offering pick up at Napoli Centrale station or at the port. On the page for €10 bus service, that still only picks up at the airport.

Posie,

You could perhaps use a "combination" approach, using train from Rome to Naples and then arrange a private transfer for the trip to Sorrento. In a jet-lagged state, that would probably be a much easier and more comfortable option, albeit more expensive. You likely won't be too enthusiastic about schlepping bags downstairs to the Garibaldi station and then the hot and possibly crowded one hour ride on the Circumvesuviana which as mentioned above has a bit of a "reputation" for pickpockets and scammers.

I haven't checked recently, but believe the guidebook lists some reliable services such as the Monetti Taxi but you'd have to contact them for prices. If you're travelling with a cell phone, you could call them when you arrive in Rome and tell them which Freccia departure you're using, and they should be waiting for you when you arrive in Naples.

Are you clear on the trains you'll be using from FCO to Naples? There are a few important things to be aware of if you haven't travelled by train in Italy before.