Getting from FCO to port

If the port is the saeaside town of Civitavecchia you can take the FL1 train from the airport to Rome's Trastevere station and transfer to a train to Civitavecchia. Prices from 11 to 30 € pp, depending on the type of train you take at Trastevere.

Trains are ok if you can all pack light and Lift the suitcases by yourselves; otherwise the fixed taxi fare is around 120 € per car. 3 cars would cost you 360 €, or 36 € pp

I'd get a private transfer, something like this: https://www.viator.com/tours/Rome/Civitavecchia-Private-Transfer-Rome-Fiumicino-Airport-to-Civitavecchia-Cruise-Port/d511-5476FCOROMPRT It's $270 for 8 people, you get your own private van which will have room for luggage, etc. Then the remaining 2 people can get a taxi that is instructed to "follow that van." Or there probably are private transfers that hold all 10 people. Trying to get 10 people on a train sounds difficult, depending on age and mobility - some can manage it, and some can't.

HOWEVER....if you are landing in Rome and going straight to the port, with your cruise leaving that same day...I might be tempted to take the cruise line shuttle, simply because if there is a delay you might still be able to make the ship. I am very uncomfortable flying in the same day as my ship leaves, esp. if it's an overnight/international flight or one that connects, because there's so many places that delays can occur.

If you are coming in to meet the ship, you are foolish not to take the ship shuttle. They will meet you and handle all of the luggage. Civitavecchia is probably 60/70 miles from the airport. The train ride is too long and inconvenient since you have to go into Rome and back out to Civit... The ship shuttle will take you directly to the ship. I don't think the private shuttle can do that. Will drop you are the port entrance.

--- I don't think the private shuttle can do that. Will drop you are the port entrance.--

NOT TRUE. Licensed Private transfer services will drop and pick you up right on the pier near your ship.
We got picked up by our shuttle service right on the dock right by the disembarkation tent.

Unfortunately, I can't remember the name of the service. Look at the TripAdvisor and read the reviews. That's where we found ours.

Thank you very much for your replies. It gives us a good idea to discuss since 4 of the group are kids aged 16,13,9,and 1-1/2.

It was true but it may not be true today. We were dropped at the front entrance and had to take the internal shuttle bus to the ship check-in point. Now that was before they redid the entrance area. We have not used Civit.... since the entrance area was redone.