With what you just told us most of us will assume:
- You will have more than just one carry on bag.
- You will arrive after an overnight flight.
- It will be highly likely that you will have some jet lag.
I am sure I will not be the only one to suggest that you forgo taking your luggage on the train and then somehow getting to your hotel with your luggage. (Assuming #1 from above)
Taking an airport official taxi for the fixed fee of (around 48 euro) directly to your hotel could be the best money you will spend on this trip. (Assuming #2 & #3) A limo service can be prearranged. A limo to the port might be a good thing also. They can take you directly to the cruise check in area. The train station is a couple of shuttle bus rides from the cruise terminal. You will have less jet lag but a limo is a lot less hassle. IMO. The cost would be about the same as from the airport.
I have used Bob's Limo several times. I found him on the internet.
A hotel in the Termini area would be good. The Termini is the starting point for many of the major bus lines to all of the major sites in Rome. I get on the next bus in line for the route I want to take. This way I and can get a seat rather than getting on a full bus and having to stand in a packed bus.