Rome to San Gimignano to Venice

There's a Hertz & Avis close to Florence SMN train station on Borgo Ognissanti. Fairly easy to get in & out of the city.

Why not rent a car in Rome, take your time going up to San Gimignano, maybe stopping in at Orvieto or even Siena, then going on to San Gimi? Then, if you want, you could drive all the way to Venice. Did that in 2014 and it took about 4 hours or so. Dropped the car at that airport but you can drop it at Piazzale Roma, right in Venice. Cath the Vap to your hotel.

If you require an automatic transmission, Option 1 is the safest choice.

It is easier to rent a car at the airport lot. No threat of driving in a ZTL and no need to learn the city-center streets to get in and out of Borgo Ognissanti safely. Taxis are very easy to get outside SMN. The drive to the airport car rental lot is about 15-20 minutes.

The fastest way to San Gimignano from the airport lot is Via dei Ponte all'Indiano. Others take the A1, but it backtracks a bit for me.

Since you plan to rent a car anyhow (and rightly so, since you'll need one in SG area), I would rent it in Rome and drive from Rome. That will give you a chance to leisurely stop along the way to visit places in Umbria/South East Tuscany. Or you can drive straight non stop and be at your SG accommodations in just over 3 hours.
If you take the train to Florence, first you need to take a taxi from your hotel in Rome to the station. Then get on a train with your luggage. The train ride is a 90 min. journey (the full base fare is 45 euro in standard class). Then, once in Florence, you need to walk (with your luggage) to Borgo Ognissanti (10 min) to pick up the car (or take a taxi for about 5 min but more money). Once you stand in line and get your car, you need to find your way out of the city to reach San Gimignano (that's a 2 hours process before you are in San Gimignano).
If you rent in Rome, all you need is a taxi to a rental car location (Tiburtina station is easy to get on the freeway, but there are others that are just as easy). Then the drive is mostly freeway, unless you want to take a more scenic route for part of the trip.
But, as you can see, whether you rent a car in Rome or in Florence, you need to drive in a major city regardless.
An alternative to avoid big city driving would be to take a train to Chiusi, then rent a car in Chiusi and drive from Chiusi to SG.
To go from SG to Venice, I'd drive to Venice (Piazzale Roma). I wouldn't bother to return the car in Florence and take the train. The prospect of driving into Florence scares the c*rap of most Americans.

Thanks everybody for the great advice! I think we will opt for renting the car in Rome and dropping it in Venice. Thanks again!

"I think we will opt for renting the car in Rome and dropping it in Venice."
That is certainly another option. It just means more time on the road with you at the steering wheel. Be sure to watch those speed cameras.

Sometimes rentals can be less expensive when you eliminate airports and train stations from the mix. If you have or make time, there are many fantastic places to stop and visit along the way on a trip like this. If I had no plans to stop somewhere along the way, I would rely on the train.

Thank you-yes I think we will take advantage of a couple of stops along the way. One more question----in Rome we are staying in Campo De' Fiori and when we get to Venice we will take a water taxi to our hotel----any recommendations where to pickup/dropoff the rental car? Thanks again for all the great ideas!

If I intend to drive north, I take a taxi to the car rental garages on Via Sardegna. This is my personal preference, and I've been doing it for decades. It's very easy to exit the city walls at Porta Pinciana, and Via Pinciana/Via Saleria (SS4) leads you on your way to the A1.

In March, dropping the car at Piazzale Roma should be a piece of cake. You'll need to walk your luggage to the vaporetti docks from the car rental drop-off location. The key to doing both of these stops: be sure to book your pick-up and drop-off during "open" hours. Lots of local offices in Italy are closed for lunch and offer limited hours on the weekend. If you don't plan your trip with some care, you can easily create problems for yourself.

When I rent cars in Italy (at least once a year), I generally use one of the two consolidators below:
www.autoeurope.com
www.kemwel.com
Actually the two are part of the same corporate group after a merger, so they work the same and are very reputable. I just check the cheaper price for the dates I need. I always select their zero insurance deductible option for piece of mind (it's only about $4 extra a day)

The pick up location depends on the company you select in the above consolidators' website. I generally select either Europcar or Hertz, as they have the best price. You can check their locations in Rome in the website below. The have a dozen each, so the choice is entirely yours. You will be going north to the A1 freeway toward Roma Nord freeway entrance so don't select locations on the south side of the city. Choose a place central, like near Vatican, or Spagna (via Sardegna) or Termini, or closer to the freeways, like Tiburtina station or all the way north, near via Salaria, closer to the A1.
https://www.europcar.com/station-finder
https://www.hertz.com/rentacar/location

Venice car rental return are all on Piazzale Roma, inside the huge municipal parking structure pictured in the article below (read the article too). It's the first parking structure you see after crossing the bridge. There are more than one parking structure but this is the one you want.
http://livingveniceblog.com/venice-instructions/coming-going/venice-arrival-by-car/
Beyond Piazzale Roma you can only travel by boat (or walk).

Thank you both for more great advice!! I have booked a car from AutoEurope with zero deductible--thanks again!