Generally speaking car is always time saving but along the Amalfi coast there is a good bus service. On the other hand, the coast road is narrow, it could be really difficult parking your car and, moreover, may be you couldn't see every corner of the Amalfi coast but I'm wondering if it is worth rushing in 1 day lots of place (Sorrento, Positano, Amalfi, Ravello,...) and stay there only 1/2 an hour each. You have to enjoy Amalfi coast not become crazy rushing, looking for a car park and because the narrow roads! To have a look to the bus time table, please click on http://www.campaniatrasporti.it/sita/sita.htm .

I think you should take the train to Naples than the train to Sorrento (that could be your base) by train (Circumvesuviana http://www.vesuviana.it/orario_ol/orari.asp ). From Sorrento you can easily get to Capri, go to Pompeii (by train) and around the Amalfi coast by bus. Positano could be an second choice as base but it is more expensive than Sorrento!

Anyway, you can rent a car in Sorrento if you like.

Ciao, Marco Milan