Personally, I would lean towards the bus from the airport directly to Naples, if you can buy the tickets when you arrive and if the buses are fairly frequent. The express train to Termini and then the high speed train to Naples will take at least 2 hours, total time, and that, only if you are relatively lucky in the timing.
And I agree with Dario in terms of the prepurchase. We actually had a case where our plane was an hour early and we "flew" thru customs. We ended up on a train almost 3 hours earlier than the one I had considered for prepurchase. That amounted to a half day of site seeing that we hadn't planned. And of course, it can go the other way as well. Your plane can be late, or customs a mess. If you have to be very conservative with the time on the purchase of the high speed train, you could have so much extra time built in that you may be waiting and then you may as well have purchased the cheap tickets/slow train.