Train or plane from Civitavecchia port

It will be considerably faster to take the train. Going to the airport is ridiculous. HOWEVER ---- at any other train station or travel agency in Italy, buy a Regionale ticket to Rome from Civit...... so that you go to the Civit.. train station and grab the first Regionale train to Rome (about three an hour and will take about an hour). When cruise ships end in Civit.. the line at the ticket office ould a real zoo -- longer to buy a ticket than the ride to Rome. With your Regionale ticket in hand, validate (time stamp) in the little blue/yellow/green box on the back of the station. Watch others do it. And then get on the first R train to Rome -- there are a couple faster trains on that route but your ticket is not good for the faster trains so make sure it is Regionale. No reserve seating. Came be standing room only but you are on a train headed to Rome. Once in Rome buy your ticket to Venice on the next train.

It is roughly 3.5 to 4 hour train ride to Venice with a fast train approximately every thirty minutes. When you get to Termini there are sandwiches and grocery stores so you will have time to buy some food/wine for the train ride.

Just be aware that Italy operates on Italian Time.
You will have to wait in line at your ship for a bus to take you to the front of the port. Only one bus was running and the lines were long. Then there is a line to buy city bus tickets (2€) to the train station. We missed the train by 5 minutes on a Saturday and had to wait an hour for the next train. When we arrived at Termini, it was a 1/4 mile trek into the terminal. It was mid afternoon before we even arrived at our hotel.
Hopefully your trip up to Florence will be smoother. Trains are more numerous mid week.

I would find out if the ship has any excursions that go to Termini. If they do the price won't be that much different than taking the train to Termini and you will have less hassle. I think you can hire a car for around 60 Euro, that might be easier.

We have ended three cruises in Civit.... and the only shuttle service provided by the cruise line was to the airport. A driver or taxi to Rome will run between 125 to 150 euro. Rome is about an hour or so via taxi. The train ticket will be less than 15 euro. The key is to buy it somewhere other than Civit...

Thanks to those who answered my question. We have decided to use the ship's transfer service to the airport and fly to Venice. We will take the hi-speed train from Venice to Rome since we will be staying in Rome before flying home.