Ground Transportation in Rome

1. A Private driver booked in advance would provide a door to door service
2. Train from Roma Trastevere station to Civitavecchia. Or from the train station in Rome that's closest to your hotel. Then you can either walk to the Port, take a cab or get on a public bus.

No option seems particularly difficult; but if you have tons of luggage and you have never Taken a train, I'd just hire a driver. Obviously a car would be more expensive: Civitavecchia is 70 kms away from Trastevere and you'll have to pay for the driver's return journey'

taxi would be easiest especially if you have cruise luggage

And if you are two or more people.

Yes there are 4 of us plus we’re in our 60’s😔

There are trains from Roma Trastevere station to Civitavecchia, so if you are staying nearby and are able to carry your luggage without exhausting yourselves, it will save money to take the train followed by a taxi to the port and you will not waste time.
Otherwise, taxi the whole way is probably 150€ or so but that's not too bad once divided by 4.

Alas, Rome is famous for the distance to the cruise port. Better Travel Agents explain this upfront to their clients. Sometimes we have stayed at a boutique type hotel that includes a transfer to the airport OR the cruise port on departure. But that's a good ballpark price.

The cruise port is a considerable distance from the train station, and the half-hourly (?) frequency public bus tends to be too full to cram onto. Both limos and local taxis are most unlikely to have security clearance to enter the actual port or go on the dock. They will drop you at the port's proprietary shuttle bus station, where you find the right bus for your ship (check carefully, since your cruise line may have more than one ship in port that day.) It's possible the cruise company's limos might have the right to come nearer the ship, but of course I don't know.

We once walked from the Civitavecchia train station to the port, and it was hot, hard work, if mostly level. (One staircase.) Rick has published a route, but I found it hard to follow. Also, bumpy with suitcase wheels. The train is very cheap, but the local trains take a long time. More than one possible station available for the Rome end.

(This doesn't relate to your particular question, but the train from Rome to Civitavecchia doe NOT stop at the airport along the way.)

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