Stay in Sorrento as a home base, a nice safe town which is better than staying in Naples. There are lots of tours available through Get Your Guide of the Amalfi coast, Pompeii and Capri.
You can take the train from Naples or Sorrento to the town of Pompei and to the Amalfi coast. The train only goes to Vietri sul Mare-Amalphi.
You travel to and among the various towns on the Amalfi coast by bus or ferry.
You can take the Sita municipal bus line from Sorrento to Amalfi coast which goes to more towns. According to a Rick Steves guest, the bus tickets can be bought at convenience/tobacco stores.
Various ferry services go to various town on the Amalfi coast - use DirectFerries, FerryHopper or Omio to book. See TravelMar for schedules. Note that most of the ferries only tun from April to October.
From an Amalfi forum: "As you get out of the Sorrento train station, after you go down the stairs, there’s a kiosk from where you can also buy SITA bus tickets. You’ll need the AC4 (€ 2.90) for Sorrento-Amalfi and AC1 (€ 1.30) for Amalfi-Maiori. The bus station is another 20-30 meters distance from there. The SITA bus company publishes a list of all the places you can purchase tickets from: www.sitasudtrasporti.it/agenzie (select ‘Campania’ if prompted to choose a region). You can also further filter out the list by entering the Comune (city/town)."
You also just take a ferry from Sorrento to Capri and tour on your own. Visit the Saint Michael church on Capri for is huge mosaic floor tile.
Pastum is a bit farther from the Sorrento area - check for buses.
