There's no direct connection between FCO and Civitavecchia (except by car), expect to pay 75-100€ for a transfer for 2. However FCO-Roma and Roma-Civitavecchia are easy by train. Likewise PSA-Civitavecchia is also pretty easy by train; although a little further/
So the real answer is, do you plan on going straight from the plane to the ship (which is never a good idea in the 1st place).
I'll end this with the fact we're flying into NAP for an upcoming cruise (couldn't get a reward seat into FCO), and NAP is only an 1h10m by train into Roma as well.