trains from fco to sorrento

Buy your train tickets when you arrive; FCO to Naples requires two trains. One train from the airport to Roma Termini.
At Roma Termini you will need to transfer to trains going to Naples.

Once you arrive at Naples Centrale transfer to catch either the Campania Express to Sorrento

https://www.sorrentoinsider.com/en/campania-express-train-schedule

or the slower local commuter train the Circumvesuviana.
https://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule

Train schedule:
https://www.trenitalia.com/en.html
Then enter:
from: FIUMICINO AEROPORTO
To: NAPOLI CENTRALE
Enter the date of travel.
Enter the time in military time. Choose a time after your expected time of landing.
That will give you an idea of how many options you have when you get there and the price.
Although buying in advance gives the opportunity to purchase tickets at discount fares (called SuperEconomy and Economy) however it is risky to buy a discounted fare ticket on the day of arrival after an international flight. If your flight is delayed and you miss the specific train you booked ahead of time, your ticket is worthless and it is not refundable or changeable, the full price is called BASE price, and, unlike airplane tickets, train ticket price don’t increase as you get closer to the day of travel, they are fixed. Also trains are so frequent that there is no chance of selling out seats, so don’t worry about finding a ticket just minutes before the train departs. Simply buy your tickets when you get to the airport station. You can do so at the ticket booth with a live ticket vendor, at an automatic kiosk, or you can even use the Trenitalia app https://www.trenitalia.com/en/purchase/mobile_ticketing.html

Once you reach NAPOLI CENTRALE, look for signs to the CIRCUMVESUVIANA Commuter train. That is a regular commuter train similar to what we have in the US in major metro areas. JazzTravels provided
the timetable for that commuter train. The Campania Express is a fancier version of the Circumvesuviana train that is geared to tourists but runs outside of commute peak hours. It’s just a few euros more expensive, but nicer.

You need to gauge the risk of buying a non-changeable, non-refundable Frecciarossa ticket after an international flight, to save two hours on the Rome-Naples ride. The walk-up fare is much higher. People who have never used public transportation at home tend to be intimidated by the Circumvesuviana. It's one escalator down, in the very modern Naples station. No reservations for the standard commuter version.