Just back from a week on Costa Victoria and thought I would share our experiences of transfers. We used a low cost airline to fly from London to Rome Ciampino airport, then hired a self drive car to drive ourselves to Civitavecchia - one way car hire about £30. Car pick up at the airport is easy, the car park is about 300m from the terminal. Navigation is easy, follow the signs initially towards Rome Fiumicino airport and then to Civitavecchia - it is about an hour's drive. We drove right into the port to the cruise terminal, checked in and left all our bags ready to be loaded, then drove back out of the port to the car hire depot. We used Sixt, their depot is about 1/2 a mile from the port gates. The only issue we had is that we were there during their lunch time (13:00 - 15:30!) and they don't have a keys drop-off box! Eventually we negotiated to leave the keys with the car service garage next door. A 10 minute walk back to the port gates and then used the port shuttle coach service back to the cruise terminal (that is about 1.5 miles within the port area!). If it did it again I would just drop bags and passengers at the port gates, leave them to wait while I returned the car, walk back, and use the port shuttle bus to the cruise terminal. And beware of car return drop-off times!.
On the return journey we used the train to Rome Termini and then the coach tot he airport. The train station is 400m from the port gates - just walk straight ahead along the prom - but why doesn't the port transfer shuttle go to the station? We were lucky, found an "entrepreneurial" man with a luggage cart offering to push all the bags for EUR 1. The fast trains go about twice an hour, but make sure you get a ticket for a fast train - we hadn't and so had to pay the supplement on board. It is still only EUR 12 per person. From Rome Termini there are two competing coach services to Ciampino airport from right outside (alongside platform 1) - EUR 6 and EUR 8 respectively.
Hope this is helpful.