I am rephrazing my earlier question: What is the best way of transport from the FCO airport to the cruise ship dock? I understand there is a train, and then plan to walk from the station to the ship.
After rereading your rephrased question, it seems like you are open to taking public transportation to the cruise terminal from FCO. I took the FM1 from the FCO train station ( not Leos Express ) 5.50E to Roma Trastavere stop, then changed platforms for the regional train 4.10E to Civitavecchia. If you take Leos Express to Termini, not only is it twice as much as the FM1, you will have quite a long walk to get to your connecting train to Civitavecchia. By changing trains at Roma Trastavere, you only have to change platforms, (might have to navigate down a flight of stairs and back up, depending on what track the Civitavecchia train is scheduled to arrive at)
Since we had answered your earlier question with the same responses, maybe you should explain what you mean by "best". We might be able to give an answer that is acceptable to you.
PS -- Ignore the RomeWalk video -- it is misleading and somewhat in accurate.
Cheapest is the train options which have already been given here. Easiest, but much more pricey, is a car service. For a car service, we like romecabs.com. I would suggest that if you can, fly in a few days early to explore Rome and recover from jetlag and travel/luggage delays.