We just did the Med cruise in Oct. Flew into Rome a day earlier than our cruise departed. We arrived at noontime and by the time we got to our hotel and settled in, it was mid afternoon. We walked over to the Colosseum (about a 15 min. walk from our hotel) and saw the sights along the way. We met other cruisemates at another hotel for dinner that evening. By the time we got back to our hotel, we were exhauted. Jet lag set in! We had scheduled a tour of the Colosseum at 9 am the next morning before we headed to the port. The tour lasted about an hour and a half, then we went back to our hotel to collect our luggage and wait for the limo driver to pick us up. We shared the drive to the port w/ 4 other people so the cost was very reasonable. We left our hotel at noontime and got to the port about 1:30 pm.
You might check w/ the cruise line to see what time you can board the ship. It varies from cruise lines. Most of them don't let you board til around 1 pm.
You could do some sightseeing b4 you go to the ship.
We decided to stay in Rome post-cruise so we could tour the Vatican. We had 16 cruisemates that joined us and booked a private tour of the Vatican.
As far as traveling to the port by train, others have done it but I don't know how much luggage you will be carrying. We decided it would be easier to hire a limo driver to take us there and they take care of the luggage, etc. It is a 10-15 min. walk from the train station to the port, depending upon where the ship is docked.
Once you board the ship, you will have time to have some lunch, walk about the ship and wait for sailaway!