Need suggestions to travel from Vernazza to San Gimignano

Train from Vernazza to nearby La Spezia.
Rent a car in La Spezia (most rental companies are near the port, just a short taxi drive from the station).
Drive from La Spezia to San Gimignano.
If the day you travel is on a Sunday, then the La Spezia rental agencies are likely closed. In that case proceed by train to Pisa, where you take the people mover from the station to the airport. At the Pisa airport, rent a car and drive to San Gimignano.
You can return the car in Rome (many locations with all companies both in the city and the airports).
Or if you stop in Orvieto, you can return in Orvieto (Hertz only) then take the train.
More to the north, between Siena and Rome, but closer to Siena, there is Chiusi, where you can return the car. From Chiusi to Rome there are trains.

How were you planning to get around in the countryside while staying in San Gimignano? By car?

I would suggest that you rent a car before you get to Vernazza. Drive to Vernazza, park the car there (there is a lot down by the beach, though don't leave any belongings in it though), or if your hotel has parking, you can park there of course (contact them now to see if they have any parking spaces available). Then drive from Vernazza to San Gimignano; it's a pretty drive, and you can stop on the way, if you like, to visit other towns or just to enjoy the beautiful scenery.

You could take the train to Florence (I don't think there's a train to Siena), and rent a car from there, but IMHO that's extra time spent buying train tickets, getting to the train station, all that.

If you want to return your car before going into Rome, two ideas are: (i) drive to Fiumicino airport, outside of Rome, and drop your rental car there); and (ii) drop your rental car at Orvieto, a town worth a visit as well, and take the train into Rome from there.

Enjoy!

Staying in a farmhouse you need a car for that portion anyway so getting a private driver to get there makes no sense.

I think the La Spieza plan Roberto outlined would be better for most.
If your hotel/bnb/apartment is in the town of Vernazza, you can forget about it having a parking spot.
It is usually not advised to drive to or try to find parking in Vernazza, parking lot down at the beach??? Not Vernazza.

I drove to Manarola and that was easy but heard from there to Vernazza is not and the Vernazza lot fills up fast.
I didn't find the drive from say La Spieza to the Florence area very scenic at all, assuming you will be taking the highway.

Thank you for the advice. It sounds like renting the car is the best idea. I picked my accommodations based on friend's recommendations and apparently my friend who stayed there was with a large group and hired drivers to take the group on tours. With there being only four of us that doesn't seem to make sense because the quote I got seemed ridiculously high. I would prefer not to do a lot of driving because it sounds like find a parking spot is an issue for a lot of sights. I know I need to get an international driver's license. Any advice on renting? Should I reserve it now?

Drive to Vernazza, park the car there (there is a lot down by the
beach, though don't leave any belongings in it though), or if your
hotel has parking, you can park there of course

The above is Fake News. There is no parking at the beach in Vernazza. Parking in Vernazza is very limited and there is a very narrow road to reach the town. It's not advisable to rent a car while staying at the Cinque Terre, because the car cannot be used and it would need to stay parked either in La Spezia or Monterosso or Levanto at about 15-20 euro a day (plus your car rental fee for each day). The most sensible thing to do is to rent in La Spezia as I told you above.

RENTING A CAR IN ITALY

I generally use RENTAL CAR CONSOLIDATORS:
www.autoeurope.com
and their sister company
www.kemwel.com
They are part of the same group, but check prices with both since the sometimes prices differ a bit and therefore I pick the better deal in either site.
They work with the largest rental companies in Europe, such as Avis, Budget, Europcar, Hertz, etc.

CAR INSURANCE: Italy does not allow you to decline insurance. However one can choose zero deductible or not. I also always select the no deductible insurance option (a.k.a. ‘no insurance excess’) since my US car insurance does not cover me abroad. It’s a bit more expensive, but the deductible can easily amount to €1,000 or more. Also coverage provided by many credit cards excludes Italy (and a handful of other countries), therefore your credit card may not cover your deductible either.

RENTAL RETURN STRATEGY: I’ve rented through both consolidator websites above (generally selecting Europcar or Hertz as the rental provider, as they tend to have cheaper rates). When you return the car make sure you obtain receipt that you filled your tank (I also take a picture of the dashboard showing the full gasoline gauge). I often get charged for fuel charges after the fact when I’m back home and having those records allow me to dispute the extra charge with my credit card.

CAR SIZE: I usually rent economy size when it’s generally for just me and my wife. For 3 people I recommend a compact car as it has a bigger trunk. For 4 people a midsize is probably necessary because of the luggage. For larger groups (up to 9 including driver) I recommend renting multiple vehicles (if there are a couple of people available to drive). Renting a minivan is generally extremely expensive. A minivan rental costs as much as renting 3 economy size cars.

PICK UP LOCATION: Picking up at airports costs more because of airport fees. However if one needs the car right away upon landing, it might still be the way to go, rather than incurring the taxi cost to reach a city rental location. Picking up at airports generally costs $30+ more per week compared to a city pick up.

IDP: Don’t forget that to drive in Europe you need an International Driver’s Permit (obtainable in 10 minutes at any AAA office with $20 and 2 passport photos). The IDP is a translation of your home driver’s license in multiple languages.

GPS: I also recommend to take a GPS unit from home with European maps loaded on it (Maps available on Amazon) and an old fashioned paper map for planning your itinerary and also as a back up since GPS navigators are sometimes inaccurate. You can buy a map locally.

TRAFFIC RULES: Google ‘Road Signs in Italy’ or ‘European Road Signs’ and read the related articles in Wikipedia or other websites. European road signs are straightforward symbols, but it doesn’t hurt to read about it. One thing to remember is that on freeways one cannot cruise in the left lane. The left lane is passing only. You also cannot overtake a vehicle using the right (slow) lanes. You must overtake vehicles only on the left.
Right turn on a red light is NEVER PERMITTED.

ZTL: Many Italian cities, such as Florence, Rome, etc. have so called Limited Traffic Zone within the city center. Inside these areas only residents can enter and park. It is therefore a very bad idea to have a rental car while staying in these cities. A better option is to rent the car AFTER visiting these cities, or return the car just BEFORE visiting these cities. Another option is to stay outside these cities and visit them from outside (basically one would park the car in a parking lot outside the city centers).

Roberto thank you for your detailed recommendations! Do you think I should drop the rental car off in Rome or pick a location outside of Rome and take a train from there? I feel a little intimidated to drive into Rome. I live in the Los Angeles area so I am used to traffic but not knowing the language I am a little worried about navigating into the city. We will be staying in the Pantheon area not far from the Vatican. I saw dropping the car at the Tiburtina Rail Station was an option. Does that seem realistic or should I plan to drop the car further outside of Rome? Any advice would be appreciated.

Someone from a big city shouldn't fear driving in Rome. Knowing the language is irrelevant. Traffic signs in Europe are symbols. Just Google traffic signs in Europe or Italy, then learn the symbols. They are largely self explanatory. There are plenty of rental offices away from the city center which are easy to reach without getting into Rome too much. Tiburtina locations are close to the freeway exit there.