Order train tickets in advance or at the station

You can get them for less than half price (€19 instead of €43) if you buy them now. But you will be committed to a specific train. How much is the flexibility worth to you?

If I were you I'd wait and buy in the moment in case you want to leave earlier, later, or get delayed. I missed a train that I'd bought a ticket for and then had to buy a second ticket at full price. Sometimes trying to save a couple of bucks can end up costing a lot more.

Definitely wait. You can purchase them a couple days before the actual day you want to travel at a Trenitalia ticket both in any station.

I would not wait until just before boarding to buy tickets. There are often long lines at the ticket counters and even a short line (1 or 2 people) at a machine can take a long time - you'd be surprised how many people just keep doing the same wrong thing over and over at the machine, or use it to look for train schedules. The other reason is that at busy times the trains sell out, especially in second class. In May I wanted to go from Bologna to Florence (a Friday around 3 p.m.), the next train was completely sold out and my choice was to buy 1st class for the following train or 2nd for the train after that.

Those are the trade-offs, summarized in four comments.

The key thought you should have is do I know that I want to travel at a specific time and date. If yes, then buy ahead. I used the trenitalia website for the first time last year and traveled with my family from Milan to Venice, to Florence, to Naples and then to Rome. All tickets purchased ahead and all went perfectly.

If I understand your note, you are heading TO THE airport. If you are thus departing, you already have a fixed time you have to be at the FCO airport. Most websites recommend 1 1/2 to 2 hours for an intra-Europe flight and 3 hours for an international flight. If your arrival time to be at the airport is already fixed, I'd probably buy tickets in advance. (if you were coming from the airport and heading to Naples, I'd advise AGAINST buying in advance)

More concerning to me would be WHEN your plane is leaving. For an international flight outside of Europe, getting to FCO from Naples for an early AM flight could be difficult, if not impossible. First, there are NO direct trains to FCO from Naples. You have to connect at Roma Termini, so the journey is 70 minutes + time waiting to connect + 31 minutes on the Leonardo Express. So journey time is probably about 2 hours, and then the hike into T3/T1 or the shuttle to T5. You would have to add all this "travel time" to your 1.5 - 3.0 hour recommendation from the airlines... Certainly doable, but risky if there are train delays.

I'd have to know more about your departure time before making an proper decision... not just on whether to buy in advance, but to train "on the day of" AIR travel.