I second the not driving. When we were in Italy, we were told the worst drivers were in Naples. And if you don't speak/read the language, I'm sure that makes it even worse! Have you checked out the TripAdvisor forums? Chances are, someone has asked your question. I find those boards so helpful when planning a trip. I have no other advice, though I'm jealous.....we didn't get to the Amalfi Coast on our trip.
I haven't been to Ravello, but I took the Circumvesuviana local train from Naples to Sorrento, then taxi to Positano. It worked out really well and wasn't too pricey. At the Naples train station you just have to walk like you're on a mission and don't wear any jewelry. Once you get to Sorrento it's super safe.
If you're including Rome there's also a bus between Sorrento and Rome called the Marozzi. I took it on the way back and it was great, safe, also not too expensive.
Beautiful area - have fun!