Trying to research how to get from cruise ship to Rome center. Taxi? Train?
Rick, and other experts often have a web page titled something like "Rome In A Day", which may be a full program (at desperately high speed) that you are looking for.
I would NOT take a taxi because they are extremely expensive and take longer than the train due to Rome's horrendous traffic (but consider a taxi if you have a tremendous amount of luggage). I would take the shuttle bus from the cruise port to the Civitavecchia train station and then a train to Rome Termini--it's much cheaper and faster. One minor warning: The arrival platforms at the Rome station are way back near the end of the building, so be prepared for a long walk to the taxi stand.
We have used Rome Cabs (not a taxi company) to book a transfers to cruise port and to and from the airport. Would highly recommend.
Several Youtube videos showing how to do it
Go to the Roll Call on CruiseCritic for your ship and sail date. You often can find people looking to share the cost of a private transfer.
The train is easy, and if you buy second class tickets, it should be under 10-12 euros per person return. Give some thought to where you want to start your day in Rome: On most of the regional (slightly slower) trains you can get off at Roma S. Pietro rather than Roma Termini, which is 20 minutes further. If you're starting at the Vatican, this would make sense. If you're starting with the Colosseum, then Termini would be better.
Take a look at how many ships are in port the day you're there. There may be a LOT of people on the move at the same time. We've done this many times. One year we were there in July (HOT!) and sprung for first class tickets on the way back to ensure we had seats on the exact train we wanted. It was a few Euros more to make it back to the ship with no stress in plenty of time.
Happy planning!