So many good questions. If you plan to rent a car, than stay out of Rome and rent your car at the airport. Most of the rental car companies do not charge a one-way drop charge as long as you drop the car within Italy. The closest rental car office tothe ships in Civitavecchia is Hertz, which is only a 3 block walk from the port entrance where there are free shuttle buses to the ships. Now, the tough part. Driving to the Amalfi coast is a bit complicated (especially around Sorrento) so you would want to have a GPS to make life a lot easier (you can probably rent a GPS from Hertz). Another rental car company that works would be Europcar, but there office is a bit further from the port (a long 10 block walk or a taxi). Driving the Amalfi drive is fun (at least for me) but trying to park in or near Positano is not for amateurs. Many park along the upper Amalfi Drive but you can find yourself more than a mile from the town. There are a couple of pay parking garages down in Positano (there is only a single one-way road that winds through the town) but it can be very expensive to park. Public transit along the Amalfi coast is possible by using the SITA bus from Sorrento, but the buses can be crowded and not always convenient. There are some jet boats/hydrofoils that run from Sorrento to Positano and/or Amalfi, but the run infrequently and you need to plan carefully and work with the schedules. By the way, getting to Sorrento on the train is possible, but you must first take the train from Rome to Naples and than change to the private Circumvesuviania Train Line.