First timers - Rome (FCO) to Lucca

You really don't need a car for the day trips you listed. Lucca to Pisa by bus or train is easy. CT will take longe,r, but once you are there, the car will probably be left in or near the biggest towns and you'll be taking the train among them.

Check Trenitalia.com, start with Fiumicino Aeroporto to Lucca. There will be a change of trains (only one change if you can catch the 11:08 direct from FCO to Firenze SMN). Use Italian station names (Monterosso for CT), change the language to English (flag choices are pull-downs at the top of the page). Ask more questions as needed.

The sensible thing is to take the train to Lucca. The website of the Italian railways www.trenitalia.com/tcom-en shows you the connections. They all involve a train to Rome (Termini or Tiburtino station), an express train to Florence, and there a change to a regional train for Lucca.
The ticket comes cheaper when bought in advance, but they are tied to a specific train. When your flight is late, the luggage is slow with coming on the belt, or whatever, that ticket is worthless. Better is to buy a ticket at the railway station at the airport. (You won't have this problem for the journey back from Lucca to Fiumicino.)
You won't need a car for all your day trips. Pisa is well served by train (less than half an hour; you can get off at Pisa S Rossore).
The same is for the Cinque Terre, giving you the opportunity for walking from one station to another, without the trouble of parking a car.

Tom, there are two direct trains daily from FCO to Firenze SMN.

Is this where you are staying? It is rather out in the countryside it seems and you will need a car. Of course you can drive from FCO but it is over 4 hours. Might be a tough and dangerous thing to do after an overseas flight.

The hotel offers a transfer service from Florence and Pisa. You could take the train from FCO to Florence and have the hotel pick you up, then rent your car in Lucca. The hotel even has a link to Hertz in Lucca. Maybe they could shuttle you there the next morning to get your car. There are lots of trains both direct (11:08 and 15:08) and with a transfer at Termini in Roma. Even a week out the fares are from Euro 27.00-47.90.

All responders: This hotel is 44 km outside of Lucca. There is no Marriott in Lucca AFAIK.

44 km outside of Lucca
That changes it all.

I would purchase your train tickets at the Airport after you arrive. There is a maned booth that handle your travel to Lucca. Several years ago we booked travel from FCO to Venice; no issues at all; just a change of trains in Rome. As for Lucca to the hotel; the hotel shuttle. Much cheaper than a cab.

Appears a train to Lucca/Pisa is preferred? Then a car or hotel shuttle??? Seems local shuttle is as expensive as car/day per hotel website.....

The hotel is not near the city 44 miles north.(Barga, Lucca)
https://www.marriott.com/hotelwebsites/us/l/lcvbr/lcvbr_pdf/drivingdistance.pdf

You have a lot of research to do now, like learning about ZTL's, and borrowing or renting a GPS to make daily navigation pleasanter. But, before learning that the resort is not IN Lucca, you were getting good advice. A car in CT is a distraction and boat-anchor, rather than a convenience, as it is in, say, Tuscany.

I recently drove back (to FCO) from Tuscany, and found the controlled-access highway to be easy enough driving, but of no "value" from a tourism point of view. I'm glad you don't have to drive INTO Rome, which would be crazy. Because we rented in Civitavecchia after an early morning cruise arrival, we stopped at Viterbo and Orvieto on the way to mid-Tuscany. But you might not have time (or jet-lagged energy) for stops along the way. (Not saying you should hit those towns .... Interests vary.)

Since our objective was at least two Tuscan hill towns a day, and some pre-reserved winery lunches, we had to have a car. But looking for parking was annoying, and the looming ZTL signs around each town scary. We had our own GPS, but that doesn't tell you how far you will have to walk after you park. I took the extra CDW so I wouldn't have to think about sideswipes in the parking lot, about $26 Euros a day from Budget.

It's interesting that you mentioned Pisa but not Florence. Although I agree with Rick (our host here...) that you should "assume you'll return", I wonder how much planning you have done. I don't mean that to be critical, but only to point out that you can't see everything in 5 nights? 4 nights?

Appears a train to Lucca/Pisa is preferred? Then a car or hotel shuttle??? Seems local shuttle is as expensive as car/day per hotel website.....
The hotel is not near the city 44 miles north.(Barga, Lucca)

It is 44km, not miles, so about 27 miles, a fair piece.

Are you using points to get a Marriott property "free? Sometimes the price of free is inconvenient. Yes, the shuttle is expensive. Maybe you could take the train to Lucca via Florence. It will be a bit of a shlep when you are jetlagged, so hopefully you can get the direct-no-changes train at 11:08 from FCO. You will still have to change at Florence for the train to Lucca. Then you could get your car in Lucca and only have 27 miles to go.

If you are going to your Marriott hotel directly after landing (i.e. you are not spending any days in Rome), rent a car at the airport and drive to it. It's about 3 hours' drive.

The Marriott is in Garfagnana, a rural valley north of Lucca, therefore you'll need a car there.

I wouldn't bother with a train at all, because eventually you need to rent a car anyhow. The alternative to go to Tuscany by train and rent a car from there is not desirable. First of all you need at least 2 trains to get there from the Rome airport. And then where do you go? there are no rental agencies at the Pisa station (you'd need to go to the Pisa airport by bus), there are no rental places at the Lucca station at all (you'd need to go to Pisa airport, even farther), and there are no rental offices at the Florence station (you'd need to walk to Borgo Ognissanti, with your luggage).

Rent at FCO and drive from there. No driving inside Rome is required. Just take the E80/A12 toward Civitavecchia, then the Via Aurelia (E80/SS1) all the way to Pisa and Lucca.

We are driving directly out of Rome - Thank you Roberto!
Thanks also for parking advice...guess we'll see how it goes...using Marriott points to stay at Marriott so we'll have to get car....

We will be returning to FCO to meet church tour group flying in on day #6 so will probably return car and stay at FCO hotel on night #5. After that we will be in Assisi and Rome with group.

Hope to enjoy Tuscany...but know it can't 'be done' in 4 days. Maybe one day in CT, 1 in Pisa/Lucca, 1 in Florence...but really looking forward more to the countryside/coast/wine...more than the cities since I'll be in Rome for 6 days...thoughts for scenery vs cities?

How do you prearrange wine luncheons...suggestions for 3rd week of September? Did you do this through Cruise line?

Driving from the Rome airport is definitely your best bet. Barga is lovely and it is only 20 minutes from Lucca. Be sure to stop at the Antica Locanda di Sesto for a meal on your way from Barga to Lucca. It is fabulous.

I asked our luxury small hotel to select and book winery lunches for us. That's taking a chance! You could try the Marriot's Concierge, or do your own online selection and booking. Our lunches ranged from 30 to 50 Euros Per Person for white tablecloth fine dining, worth it for us. We had some mediocre lunches in the tourist hill towns themselves, sad to say. And we followed Rick's rule to walk three blocks away from the crowds!

Most big wineries charge for tastings. Some only tour by appointment, others on demand. Some posters here would prefer small wineries with less formal policies - I mean like an Agriturismo. It's a matter of personal preference and time commitment. For example, a huge winery might make a larger variety of wines, or offer "Vertical Tastings" not available in a tiny facility.

Edit: Are you sure you want to backtrack to Tuscany/Umbria with the pilgrims? Why not go someplace closer, by train, like Naples/Sorrento/Pompeii/Capri, and skip the car hassles? Italy is a big country with lots to see.

Your home is a secret in your profile, but this is like flying into Boston and going to see the art museums in Northwestern Massachusetts, then going back to Logan airport to meet a classical music group that's going to a few concerts in Tanglewood and Williamstown!