getting from Civitaveccia to Rome

First -- type Civit... in the search box and you will have a dozen answers. Second, best and economy, and not a lot of walking doesn't go together very well. The easiest is going to be a taxi but four people and a lot of luggage may not fit and it is not high on the economy side. A pre-arranged shuttle or hired car/driver would work but still looking at a cost of 75 to 100 Euro. About an hour ride to Rome.

The train might be the cheapest -- maybe 30 to 50Euro but it is about a mile walk from the port entrance where the ship's shuttle dumps you to the train station. Another big hike to the front of the station (3 or 4 blocks) and maybe a 20E taxi ride to your hotel depending on where you hotel is. And, again, you might not all fit in one taxi. The hired car may be looking better.

If you need to avoid walking then the hired car is your best option. The prior lists I mentioned earlier will give you a list of shuttle/limo services in Rome.

There will be lots of people coming off the ship. As Frank explains, the train station is about a mile away. There are taxis but they are looking for the fare to Rome and not the train station. If you can get to the train station, most of the train runs are on local Regionale trains to Rome. The fare is 4.50Euro for a 2nd class ticket. The travel time is 1hr.-20min with no train changes. You might get lucky with the few faster trains. A bit more expensive and the trip is faster. The ICPlus train is 8.50Euro. Trains run twice an hour. Expect the train station to be crowded. Use the electronic ticket machine. Its fast and it will prompt you in English. It will also accept your American credit card. Don' worry about seat reservations on the Regionale train. They aren't permitted. It's first come first served with the seats. If no seats, you can stand.