You will LOVE the Amalfi Coast! We chose Salerno as our home base since it is a hub for buses, trains and ferries. We did go to Sorrento for the sole purpose of eating at Delfinos in Marina Grande right on the harbor. It is a Rick recommendation, and it didn't disappoint. The only reason we took a train to Naples was to go through the Archaeological Museum prior to our trip to Pompeii. It was wonderful! The next day we toured Pompeii, which is a easy train trip from Sorrento or Salerno. It might be more of an ordeal from Positano which has no train station. Positano is breathtaking from the water. Be sure to take the ferry to Amalfi and then the local bus up to Ravello! The view from Ravello is amazing. Be sure to tour
Villa Rufolo there. I think you can probably see both Amalfi and Ravello in one day, but I would go to Ravello first thing in the morning before it gets crowded as it is a small village. Then return to Amalfi to see what you want to tour. We did not visit Capri, so I have no input there. If there is any way to avoid the local train, the Circumvesuviana, I'd do it. We took it once, and it was a side show of panhandlers, unruly teens who popped on and off and has a reputation for thieves. People were locking their luggage to anything to stop thugs jumping on, grabbing their luggage and jumping off. There was no conductor taking tickets or maintaining order. I had read about this train beforehand, and we tried to avoid using it. Alas, we had to take it to get to Sorrento as the ferry was not in service to get there. Have a wonderful time!! We did!