Planes trains and automobiles, tours too.

Not sure about the order of your itinerary but assuming it’s in the order you listed
Rome to Florence (train)
Florence to Il Ciocco (train to Lucca then rental car, or rental car from Florence)
Il Ciocco to Venice (return rental at Lucca then train via Florence to Venice)
Venice to Naples (train)
Naples to Rome (train)

TRAIN
Train companies, 2 to choose from.
www.trenitalia.com
www.italotreno.it (does not go to Lucca, near il Ciocco)

www.trainline.eu shows both two companies above at no extra booking fees.
The segment from Florence to Lucca is on a Regionale, therefore no need to book. Buy onsite.

CAR RENTAL
You will need a car rental while at Il Ciocco, which is in the Garfagnana Valley near Lucca, in the countryside. You can rent a car in Lucca. Use this consolidator to find deals:
www.autoeurope.com

Excellent information, Thank You! Is this the famous Roberto of "Tours By Roberto"? If so, what is the best way to contact you Sir?

This itinerary is in sequence except between Venice and Naples is Sorrento for 3 nites. Honestly, we are searching for a company who could provide the transportation, transfers and tours that would make the most sense for hotels' lay out.
I also have an injury to my knee. I'm very concerned about steps. What is our best plan?
Any recommendations would be of help. Kindly, deb

First, I think some of your expectations may be a little off. You are not going to find a single company or even a couple that matches your travel request. You either take a tour and follow their schedule or you arrange your own. In each of the cities, you will use the local TI to arrange day trips via bus,van etc., since it appears that walking tours are out for you. Or you could use a local travel agent to arrange your schedule if you are not prepared to do it yourself. And, obviously, you need to spend some time with guidebooks -- notice plural -- and travel DVDs to determine what you would like to see or not to see.

Italy Beyond the Obvious specializes in custom trip design. May be just right for you.

https://www.italybeyondtheobvious.com/

The link I set did not work so try this one.

I believe that he lives near San Francisco, debzie. The one you want lives in Italy.

Our Roberto is pretty famous though - certainly around these parts.