Is the train a reasonable option from Livorno to Rome?

I suppose it depends on what you mean by "a couple of pieces of luggage" If we're talking about a rolling carry-on type and another small bag that you can easily lift, than it wouldn't be such a big hassle to take a train. If we're talking about 2 large suitcases you can barely get off the ground that's a whole different story. For the train, you will first need to get to Livorno Centrale, because the other station in Livorno doesn't connect directly to Rome. I assume you would be able to get a taxi to the station, but I can't comment on how much that would cost. Maybe someone else can comment on that, as well as whether or not there are stairs to navigate at Livorno Centale. From there, you would take a direct train to Rome. The fast train will have you at Termini station in about 2 1/2 hours for 53 euros (first class - recommended with a couple of bags). That's certainly the way I would go. From there, you can get a taxi outside of Termini that can take you wherever you need to go in Rome. If you will have large or heavy luggage, you may want to consider renting a car. It would be about a 4 hour drive, and you could drop the car off at the airport outside of central Rome, or at one of the locations just off the Autostada. For example, there is a car rental drop off (for certain companies) near Villa Borghese. Its not far off the highway, and you won't have to drive through Rome (because you cannot due to ZTL). Another option: If there are a few of you, hire a driver to drive you to Rome! Depending on how many people are in your party it may not be much more than it would cost for all of you to take the train.

Unless you're travelling with trunks of luggage, the train is the only "sane" travel option from Livorno to Roma. Renting a car make very little sense indeed (unless you plan to make several stops en-route to see the sights). Take a taxi from the cruise ship dock to Livorno Centrale (approx. 15-20 Euros), then any train to Rome. The best trains on this route are the reserved ES-City Frecciabianca trains, whereas the very cheap regionale trains (which take about one hour more and make several more stops) don't have reserved seats, which may or may not be an issue (depending on your day and hour of travel). If you take the ES-City train, second class is fine (36.50 Euros), considering the length of the trip (2.5 hours). The regionale train costs 17.05 Euros in second class.

Make sure you get a reserved seat, because you really don't want to be standing the whole way...I've seen it done.

I would definitely take the train. Traffic in and around Rome can be murder, the train will bypass that. I would also figure out how to travel with one carry-on bag. We do it every time, even when we plan a cruise as part of the trip; it really can be done. It's so much easier to move around when you don't have a lot of luggage in tow.