I vote for public transports in Amalfi Coast! The road is scenic but narrow and it could be a difficult drive experience. moreover public transport is well settled along Amalfi coast. At the end, but not least, it is a nightmare finding out a car park for your car!

>From Rome you should take a train to Naples and change to a local train to Sorrento (circumvesuviana company ) in the Central station (connection downstair following arrows) then catch a bus in Sorrento to all the destination along the coast.

The train to Sorrento will stop in Pompeii. Be carefull because there are 2 stops in Pompeii: Pompei (the modern city) and Pompei scavi (the archaeological site) that is the right station for you and is located just at the entrance of the old city. You can stop there on your way back. The only drawback is that I don't think that in Pompei scavi station there is any luggage left office where you can leave your luggage :-(

Ciao, Marco in Milan - Italy