Getting to the cruise ships

Here you go:
The cruise terminal is 80 kms from the city of Rome.

https://www.italylogue.com/planning-a-trip/rome-cruise-terminal-where-it-is-how-to-get-there.html

I can't see a date on this website, but I would imagine the procedure hasn't changed much lately.

The cruise port is at Citivecchia - not in Rome. the traffic is notoriously bad - but the trains run frequently, its a suburban line so you'd want to have not too much luggage

https://community.ricksteves.com/travel-forum/italy/ground-transportation-in-rome

Last September, my party of four used a car service to get to the port, I believe the total was 160 Euro, which split 4 ways made sense for us.

Train service is good, but a car service is more comfortable. Avoid the cruise transfer option. It’s an unnecessary expense and not particularly pleasant to boot.