We will have adequate time to transfer from FCO to Civitavecca(Rome cruiseport). What's the most economical way to do this?
Depends on what you mean by adequate. Plan on at 5 hours if you use the train. Could be as short as three but that depends on everything clicking. Most economical is the train.
I would guess that the train would be the cheapest. It will take about 90+ minutes for the train. The thing is you will have to walk or taxi about 2 km from the train station to your ship depending upon which berth.
We opted to arrange for a private transfer (Bob's Limo) which took only about 50 minutes, door to door. For us last May, the transfer was €150 for six people. Alternatively, you could grab a taxi which is about €75 if I overheard correctly.
You can google for the latest costs.
All depends on what time your flight is scheduled to arrive, and what time you have to be on the ship.