Tour ends in Naples. Want to take train back to Rome fir flight home. Should we buy tickets before tour (from home)?
You could if you are sure of the time
I hope flight from Rome home is the next day
https://www.trenitalia.com/en.html
Station names
Napoli Centrale
Roma Termini
You'll save money if you buy well ahead of time; fares on the Freccia trains are variable and will almost certainly be higher if you buy on or close to the day of travel. But be sure of your timing.
Be VERY sure of your times, most especially if you are thinking of flying home the same day. Is the flight in late afternoon? Because the total time, if all goes to plan, from hotel to airport gate would be close to 6 hours. Breakdown (assuming previously purchased tickets): 45 minutes from hotel to train; 2 hours to FCO including a change in Rome to the Leonardo Express; and arriving the recommended 3 hours before departure. And have a plan B in case of any rail disruptions on the day. Depending on your risk tolerance, you might want to be in Rome the evening before your flight.