Leaving on Sunday to catch cruise. Do the trains fill up fast? Should we buy tickets ahead of time.Rome to port.
If you mean the Civitavecchia port, those are mostly regional trains which do not sell out. Make sure you stamp those tickets in the yellow box before boarding the train.
It is a commuter run with three to four trains an hour during the week and couple less on Sunday. IF returning to Rome after the cruise buy a RT in Rome because the lines to buy tickets after the cruise can be very long especially if more than one ship in port. You can safely buy tickets when you arrive in Termini. Use the ticket machines. You will have lots of company headed to the ship.