Be sure to study Google Maps for the walk. It's a long way to the station, especially with luggage, and hot in the sun. You must train "the wrong way" to Rome before heading to Florence by train. You'll start with a free port bus, from the pierside to the port's bus center.
Edit: I'm sorry Frank, but I have done this walk. Civitavecchia is famous among Travel Agents and travelers (us ... I've been there for cruises three times ) for how far it is from Rome and how annoying it is to use. There are plenty of summer days in Rome where it is NOT cool in the morning. The reason I mentioned Google Maps is that even carrying Rick Steves' travel book, the foot route is hard to figure out (for example, avoiding stairs right beyond the port (not just at the train station) and selecting the port entrance that is closest to the bus platforms upon arrival.) Useful signage in town was non-existent when we did this walk in 2016.