David,
Just a reminder - for driving in Italy you'll require the compulsory International Driver's Permit, which must be used in conjunction with your home D.L. Failure to produce an IDP if requested can result in fines on the spot. The IDP is easily obtained at any AAA office for a small fee, and is valid for one year.
A few comments on your questions. Could you elaborate on the reasons you're using a rental car in this case rather than public transport? I tend to use rental cars "strategically" for specific purposes, but use public transport most of the time as it's a faster and more efficient travel method without the worries of parking, ZTL's, etc. (I've seen ZTL zones in towns in southern Italy as well).
In the same circumstances, I'd probably use public transport from Rome to Sorrento (ES/AV to Naples then Circumvesuviana), rent a car in Sorrento to see the Amalfi coast and Paestum and then return the car in Sorrento.
Good luck and happy travels!