Naples is the natural gateway to Sicily. Direct flights under an hour, overnight ferries while you sleep, and the train still does the Strait of Messina crossing.
Ryanair and ITA fly Naples → Catania and → Palermo.
GNV and Tirrenia run Naples → Palermo overnight. Depart ~8pm, arrive ~7am. Cars allowed. You wake up in Palermo.
InterCity through Calabria, ferry crossing at Messina. Night train available with couchettes.
Fly for speed. Overnight ferry if you have a car or want the experience. Train for romantics.