We flew to Palermo from Rome, on easyjet - fast and relatively cheap. For you, I presume either a flight or ferry option would require departing from Naples, so you'd probably want to take a train to Naples, then head out to Palermo from there, but the ferry boat will take much longer, and may not save you any money.
Unless you already have a car on the mainland and really want to have it with you on Sicily, flying would be my recommendation. You could always rent a car (as we did) once you landed at the Palermo airport.