Several of Rick's books have a multi-page answer to your question, with specific attractions to fit the very limited time. Maybe you can find one in your public library, the info doesn't go out of date. It's really worth reading, as a sort of "reality check."
It's not really necessary to buy this local service train ticket in advance. I'm not even sure the ticket is specific to the train. But it's really cheap as a walk-up fare. You may wish to consider the overpriced cruise company shuttle bus, especially if they promise that it will pick you up beside the ship. The point is they guarantee that the ship will wait if you are on the bus at the appointed RETURN time, in Rome.
Some of the things you want to see, like the Coliseum, may have required advance, timed ticketing.
I'm handicapped in part of the answer because our small, 300-passenger ships did not use the modern cruise "terminal" at Civitavecchia, and we had to wait beside the ship (on the pier) for the proprietary, required, free shuttle bus to the bus-circle at the exit from the Port. I have heard of shuttles to the train station, but I don't know if they leave from this circle, or from a pier, or the terminal. Note that you have to think about the number of "seats" you might need to get all the way back to the ship when you return. It only counts if you are ON the boat at departure time!