We are arriving in Naples via Eurostar. What is the best way to get to Sorrento? Cost is not the priority, rather a nice scenic view, but sort travel time as well.
The obvious choice is to take the Circumvesuviano train. This is a commuter train, and it may appear a bit gritty (certainly after the Eurostar), with some grafitti, but it's quite safe as long as you keep your wits about you and pay attention - same as on any other urban train. It's quick, cheap and efficient - and I'd even call parts of the trip scenic.
you might look into (curreriviaggi.it) They have a shuttle service, Naples to Sorrento, 80E for up to 3 persons, additional P/ are 10E. I know they pick up at the airport, but not sure about the train station.
The shuttle from the Naples airport is €10 per person one way. Of course, you would have to get to the airport. How about the hydrofoil from the Naples port?
Re David's post: similar experience. Price is right. Local color and scenery. Be alert. Read RS closely: good advice.