A question about the train from Termini Station

Check at the Trenitalia website. The 13.00 Regionale veloce is a direct train, taking some 2,5 hrs at the cost of EUR 46,20 for the four of you.
It would be best to buy those tickets the day before to avoid a possible queue at the moment your train is about to depart. (Make sure you get the tickets for the right day. And don't forget to validate them at one of those small machines before boarding the train. You don't want to be caught with invalid tickets.)

The Regionale Veloce train is almost as fast as the Freccia train on this specific route, so I'd choose the less expensive one, but that's up to you. (Actually read my edit below)

You can see the train's route and the number of stops it makes by clicking on the little grey circle icon with a white "i" in its center, right by the train number.

The tickets I found on the Trenitalia website run €11,55pp each way.

Have a wonderful trip!

Edit to add:

I'd suggest taking the direct Regionale Veloce train (departing Roma termini at 9:00 or 1:00pm) instead of the Freccia/ Regionale/or Intercity train combination which involves changing trains.

Thank you for the great info. The only trouble is we are flying the day before. I have read that it is wise to wait til we get to the station to buy the tickets in case our flight is delayed. We are being transferred by van from the airport to the Termini train station so there might be time delays there as well. OR, could we buy the tickets at the airport for the train leaving the Termini Station? Would that be helpful?

I often buy the regionale or regionale veloce tickets online just to avoid stopping at a kiosk (they can have lines, too) or waiting in line. Print out the tickets at home and just show them to the conductor. You don't need to validate them if they are print-at-home, they won't fit in the machines.

Zoe. Would these prepaid online tickets be valid for the day or for a specific time? Since you don't have to validate them I assume they are good for that afternoon? Thanks

Why do you need a van? You can catch the train at the airport station in front of T3 and change at Roma Tiburtina.
What time is your flight arriving?

Regionale tickets purchased on line can be used on the booked train and on any other regionale doing the same route and departing within the following 4 hours.

All kind of Trenitalia's tickets can be purchased at any Trenitalia station and at travel agencies displaying their logo on the window.

Regional trains tickets can be also purchased at many tobacconists, but these days most people get them via the official app around one hour before departure.

Roberto
For about the same price as the train we decided to get picked up and driven to Termini. We thought it would be easier. How long a drive is it to Termini from airport?

You need to specify a date, at least.

Zoe. I did.