We agree with most everything that Jim says except it is very difficult to ever beat the crowds at the Vatican. The Michelin guides are good, Rick Steves is also good, but we do not always agree with the books. When you plan your day in Rome (and Florence) you must be real cognizant that you are more then an hour away from your ship which is leaving that same day (whether you get back or not). For independent planning on cruises, you must always keep this fact in your mind and plan a strategy that maximizes your fun while minimzing the risk that you might miss the ship. We do agree that the Vatican lines are usually shorter in the afternoon (although this is not always true) but, assuming this is your first priorty in Rome (it should be) you cannot take the risk of big afternoon crowds spoiling your chance to fully appreciate the vatican museums. Once you are inside the Vatican you are in a lengthy maze of corridors and walkways with the prize (Sistine Chapel) at the end of the tour. We know some who have gone through this tour in 2 hours, and others have spent more then 4 hours.
At the end of the day, you will need to go to the train station (probably the Termini station) where it is a very long walk from the entrance to the track where you get the train back to Civitavecchia (we are talking nearly 15 min of just walking inside the station). Unfortunately, that particular train uses the tracks that are about as far as you can get from the entrance (you won't find this info in most tour books) so you need to give yourself extra time. There is also the possibility that a train can run late, so you should never rely on taking the last possible train (we like to get back to Civitavecchia at least 1:15 early. All this means you need to get into the Vatican during the morning.