Certainly Salerno is a sensible place to get to Pompeii with many regional trains going direct to Pompeii Scavi-Villa dei Misteri. Salerno is also better as a starting point for train journeys either down to Sicily, or up to Rome/Florence/Bologna/Venice.
Pompeii and Sorrento are served from Naples by a somewhat quaint rail service from Naples (Circumvesuviana train). It is not included in the Interrail network. Herculaneum is on the same line. The station is just below the main station.
Obviously there is a shuttle bus from the airport to Naples Central station. Then there are plenty of local trains not needing reservations to Salerno - avoid the Freccia and ICs - it is only about an hour train ride.
In IT any train marked as TrnItlaia will accept your pass. The tiny other trains mostly also have special barriers that will only acccept their own stuyle of tickets-BTW thse are fairly cheap in this area. There are also a few ride-at-will regional tickets available. A passday will cost an awful lot more as just a single Napoi-Salerno.