Rome to Cittavechia port

Welcome to this newsboard, ekuk. You will get a better reply if you define "best". You have not told us about your physical abilities, budget, health, free time in Rome, or experience with public transportation. Are you going directly from FCO, or from an overnight in Rome? How many in your party? Is your ship boarded from the cruise terminal building? Month of travel?

https://community.ricksteves.com/travel-forum/italy/rome-airport-to-port-outside-of-rome

https://community.ricksteves.com/travel-forum/russia/termini-station-to-civitavecchia-cruise-ship

I will be in Rome for a day before my cruise from Cittavechia. Arriving Rome by train. From Rome to the port I opted for a private transfer (scheduled ride booked by a travel agent). Your hotel or cruise line may offer the same. It's expensive, but we get door to door service, with no luggage handling by us! You can also take a train(about an hour), then bus or cab to your ship from the train station.

hey hey ekuk
"best" means different options to everyone. my opinion is to hire a private cab "romecabs.com" pick up at your hotel, luggage in trunk, sit in comfy seats and enjoy the ride. you have spent enough for this trip & cruise, don't be scimping for transportation. how long will you be in rome before cruise? hopefully not arriving day of or day before, coming from USA/Canada, dealing with jetlag.
you haven't offered any info as Tim mentions which would help these posters give you more info "who what where when & how"
the port is more than an hour away. many others that are cruising will be looking for budget transportation, train/bus/shuttle, all trying to get to port at same time, not worth stressing out or worrying if room on transport, how far to walk to where boat is docked at, not worth it.
years ago with protest happening in rome, streets all blocked off near piazza navona, cops with their guns & tanks everywhere, we got lucky to find a private driver in his own cab, was not really allowed to port but he took us for 140E right to ship. several people missed the ship's departure and weren't happy. one of best euros we spent
spend the money, get there safely and enjoy your first cocktail/wine with some food and enjoy the sailaway. have fun & enjoy
aloha

The train is economical, but a hassle if you've got anything bigger than a carry-on. The cruise line often offers transfers, but I've seen them as much as $100 pp. It easiest and most pleasant to have a driver pick you up, tuck the bags in the trunk and whisk you (in about an hour) to the port. Gets your vacation off on the right foot, I think. But, you might also want to post in your roll call on CruiseCritic. Sometimes people put together mini-transfer vans holding 5 or 6 people. Cheaper than a private car, but it still gives you that "I don't want to think about it; I'm on vacation." experience. If you've booked with an agent, ask him/her for recommendations. No sense in reinventing the wheel.