transportation choices

If you are flying into Naples the bus might be an easy choice. Private transfer will cost you about 100 euro. I really like the ferry however - relaxing, a beautiful start to my time in the area. When leaving Capri the only real practical choice is the boat to Naples. Then taxi to the train station. Easy!

I can't really answer your first 2 questions. Depends on time if day, how many people, how much luggage and what's your budget.

The last question is easier. Take the ferry from Capri to Naples, then a taxi ride to the train station. Couldn't be simpler. Otherwise, you'd have to take the ferry to Sorrento, then a bus/train/private transfer to the train station in Naples for the train to Rome. Why?

Thank you for answering.

To clarify. There are two of us. We fly into Naples at 3:30 pm. We have one bag each.
We will have been travelling for a long time at that point.
We will get up the next day and go to Positano late morning.

We figure we would end up hiring a private transfer on one of the legs
(to Sorrento or to Positano) but if it is easy to transfer using
the bus or ferry (we know it is cheaper), we would do that.

The bus from Naples airport to Sorrento should be easy: http://www.curreriviaggi.it/eng/autolinee.html.

From Sorrento to Positano, look at the location of your hotel and any advice they offer. The ferry arrives at the bottom of the town, while the bus stops are further up the hill. You probably want whichever is closer.