fastest & easiest way to get from Rome to Naples

Leonardo Express Train from Fiumicino Airport station to Rome Termini station (main station) - 32 min.
High Speed Freccia Train from Roma Termini to Napoli Centrale station - 70 min.
(allow at least 20 min. to transfer trains at Roma Termini).
There is no need to book anything from the US. You can buy tickets when you arrive at the airport station. That's actually the best option because you can't predict whether your flight will arrive on time.
There is a train every 30 min. from the airport to Rome Termini.
And at least 2 trains per hour from Rome T. to Naples. None of them will be sold out.

You don't need to book ahead, since trains run twice per hour, taking 2 - 2.5 hours, with a connection at Roma Termini station. I would buy the tickets there for the next trains leaving. See How to Look Up Train Schedules Online for the DB train schedule link and tips for using it. It gives you printable schedules from Roma Fiumincino to Napoli Centrale, but does not sell tickets.

So as far as I can tell, if we land at 1:15, and every thing goes well, we could be in Naples by 4-4:30ish, right?

I would say that your estimate it pretty optimistic. It really depends on how long it takes you to get through customs. When my husband and I landed at Fiumicino it took us 2 hours to get through customs.

Thanks for the heads up Morgan, everything I've read gives the time frame of 15 minutes to 2 hours! I'm hoping because of the time and day we're landing we might be ok.

Customs doesn't take any time. Passport control might take longer if several flights arrive simultaneously. But in my experience at Fiumicino what takes for ever is waiting for my suitcase at the baggage claim.

It may have been passport control, not sure. I am sure that it took us 2 hours to get out of the airport and we stood in line a lot. :) We also arrived on one of the first flights in that morning, so the bottle neck may have been caused by other flights arriving at the same time. Have fun!

Thanks, your post were all a great help! I'm getting way excited, only four hour 'til take off! Woohoo

I pack light (carry on only) and sit near the front of the plane so I'm one of the first off the plane and to the immigration line. That way I'm out quicker with less time at the airport and more time in the city.