First advice I can give you is make a list of what are the most important things for you to and make sure to save some time to enjoy the beautiful ship. I only say this because we booked excursions in every single port and I felt like we left no time to explore the ship and there is so much to see, there were things I found to do on the ship that I didn't know till the last day which was our sea day.
For the excursions we ended up booking through the cruise line only because it was our first time to Europe and we wanted to be sure to make it back to the ship with plenty of time. If I go back I will use "Rome in a Limo" I researched them before going on the trip, they had great reviews and I saw their cars in all the ports through Italy. Also if you wanted to visit the Vatican I recommend booking a tour that includes a Vatican guide, they are incredibly knowledgeable and answered all of our questions.