It sounds like you have a great trip planned. I hope you have built in some extra time at the front of the trip.
Your cruise line will have a section on its website called “port guide”, “destination information”, or something similar. It will give the cruise lines recommendations for the time that your flight should be booked after. As a general rule of thumb, take your expected docking time and add an hour for when you will disembark the ship. Will you walk off with your luggage or will you need to claim it? Add another 30 minutes for claiming luggage and port formalities. How will you transfer to the airport? Think about the method and time involved with that method. At best, the drive time is at least 50 minutes. Trains, private transfers, and cruise line transfers should be available. Finally aim to arrive at the airport 3 hours before an international flight. What time does that give you for your flight?
Look for direct flights if possible. I don’t know that anyone can accurately predict when and where irregular operations will occur with any great deal of accuracy. I’d also look for airlines with either multiple flight to/from Rome or are part of an alliance offering multiple flights.