FCO to Naples

Most of the time I would buy a ticket from Rome to Naples ahead of time because of the discount you can receive. In your case, however, I'd advise against it. There are many variables that would affect what time you should buy your ticket - your flight could be delayed, customs could take longer than you expect, and so on... Personally, I would just buy your ticket upon arrival.

Are you sure you arrive at 1:15pm? Are you having a layover in Europe somewhere? It seems a little late for a flight coming directly from the US.
In any case, these are the options from Fiumicino Aeroporto to NA C.le:
Full BASE price purchased on the spot (when you arrive) costs €57.
SUPERECONOMY price purchased ahead of time online costs €33. It's a 40% savings however there are strings attached. If you miss the Freccia Train from Rome to Napoli, you lose your money. Supereconomy tickets are non changeable and non refundable at any time. So if your plane arrives late, or if you have to cancel or delay your trip, you must say good bye to all your ticket.
ECONOMY price purchased ahead of time online costs €43. This type of ticket can be changed for a fee and with payment of the full price but only prior to the train departure time. So if your flight is late, by the time you are on the ground ready to change your ticket, the train might have departed already, and you won't be able to change it anymore, so you lose your money again.
It's up to you. What is your appetite for risk?

No way to answer your question. Too many variables. Last May we arrived around 10 am on a Friday from New York. It took almost two hours to clear immigrations. Too many planes and not enough agents. Then the train to Termini is 30 minutes plus another 30 minutes if you just missed the previous train. Another 30 mins to use the restroom, maybe purchase a quick snack, and find your train's platform in Termini. And if you happened to be that one person in a hundred that has luggage problems, who knows how you will be finding or filing a luggage claim. You can buy the ticket to Naples at the ticket booth in the airport when buying your Leonard Express ticket. AND do not forget to validate (time stamp) the LE ticket. This is one time buying in advance does not make any sense.

However, if arriving on a connecting flight in Europe then you will avoid immigrations in Rome and customs is a walk through the green door. In that case you could be in Termini within two hours. Then you might consider buying a ticket around 4 or 5 pm.

We considered the train to Naples but decided to just book a flight. We landed in Rome and transferred to a flight to Naples. Super easy and we were really happy we made that decision.

Proceeding from FCO to NAP by air with Alitalia is an option, and it seemed to have worked for Michelle.
The flight is short (55 min. gate to gate), however you must be aware that there are ONLY THREE DAILY FLIGHTS from FCO to NAP (all Alitalia), whereas there are at least two trains an hour going from Rome to Naples and the total journey (including the portion from the airport to Roma Termini station) is just over 2hrs.
In May the 3 Alitalia flights to NAP mentioned above depart from FCO at:
10:20, 14:55 and 21:20.
So if you miss your scheduled flight to NAP at 14:55 (the closest to your arrival at FCO), the wait at the airport until the next (and last) flight could be long.

I'm confused about the need to go into Rome Termini to catch the train from Rome to Naples. I thought you could get the Naples train directly from FCO. No?

Going directly from the airport is not an option. You must either transfer at Roma Termini or Roma Tiburtina. Go to trenitalia.com and check results from Fiumicino Aeroporto to Napoli to confirm the need to transfer and to see what options are available.

No. There is no direct train from FCO to Naples. At the FCO station you take the Leonardo Express shuttle train that takes you to Roma Termini, Rome's main station. At Termini you transfer to a high speed Freccia train to Napoli Central.

Grazie Mille a tutti

Thank you so much for your responses! Our flight is straight through from LAX and we will end up in Sorrento. Our tour will take us from Naples to Sorrento but they need to know what time we arrive. tThis is why Im trying to buy tickets before our journey begins, but it looks as if it would be safer to just wait and call the number for the tour to pick us up at the last minute. They did inform us that we will have to wait and the terminal in Naples for the ride to Sorrento.

I just have been reading other post. Would it be easier to just catch a taxi to the train depot in Rome when we get through customs, then buy the train ticket to Naples at the main train station in Rome? I didn't know we couldn't got directly to Naples from the airport.

Once you board the train in Rome, perhaps you can call or text your tour company and that will lessen your waiting time at the Naples station.

The taxi is a fixed rate of 48E and the train is 14E/person. Hard to judge which would be quicker. Mid-day you will have traffic to contend with so the taxi could be quicker or slower depending on what happens. But that is an option.

Are you absolutely certain about your flight? I was just on the Delta site and could not find a flight that matched your 1:15 arrival for the last two weeks of May. And no direct flights. Everything was one stop either Boston or JFK in the US or Paris, Amsterdam in Europe. The arrivals times closest to your 1:15 was 12:40, 2:45, and 4:00. And, of course, a number of AM arrivals which is more common. How about confirming with flight numbers.

Ok. barnmom.
I found out on which flight you are.
It's actually not a Delta operated flight, it's a code share.
The flight is operated by Alitalia (AZ621) departing LAX at 4:25pm and arriving at FCO at 1:15pm (next day).
Now we cleared that out, you are on the non stop LAX-FCO. Good choice, no lay overs anywhere.
If you decide not to chance it with the Alitalia flight at 2:55pm from FCO to NAP, the train is a good alternative.
Regarding the option to take the taxi or the Leonardo Express to Termini, I can guarantee you the train is faster (32 min). At that time of the day it is unlikely the taxi can make it to downtown in 32 min. Maybe 40 is more like it. Of course you might have to wait for the next Leonardo Express a bit, since there is only one every 30 min. If you were going to a hotel in Rome, I would definitely suggest a taxi, which would take you right in front of the hotel. But in your case you are going to catch a train inside Termini, where the Leonardo Express will drop you off, therefore there is no advantage in taking a taxi. Either way you need to wheel your luggage to the high speed train to Naples. Whether you do it from the platform where the Leonardo Express drops you off or from outside the station where the taxi drops you off, the walking distance is about the same (actually probably slightly farther from the taxi stand outside of the station). At most 100mt (300 ft) anyhow.

Yes, Robert! that is our flight. It looks like the best way for us would be to take the train into Rome and buy the ticket from Rome to Naples when we get there and no before. If there is a better way, please let me know. Thanks