Rome Airport to Naples & then a return to the city of Rome?

My wife and I are travelling with another couple from Canada to Rome with arrival at 0920 hrs., Sept 18, 2014. We have booked Airbnb location in Naples for Sept 18 to Sept 22nd and then return to Rome where we have Airbnb location from Sept 23 to Sept 27th. On Sept 27th we board the HRM - QE II for a 14 day cruise. We would appreciate your words of wisdom on rail transportation / tickets etc., for the airport in Rome to Naples and return from Naples to Rome. Thank you in advance and warmest regards, Raymond Scheller
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