Hope this helps others in their trip planning. Just came back from our June sailing. It was a great cruise, we (family of four) did not want it to end, it was our first time in Europe.
Arrived in Rome (FCO) at noon on Friday, and took the pre-arranged shuttle from the B&B (1 km north of the Vatican) we were staying at for 37 euros.
On the Friday afternoon, walked to the Vatican (had pre-purchased Vatican Museums tickets online from the Vatican website before leaving).