Pontedera is not commonly used as a base but I am sure you can find great agriturismos in the countryside area as nearby.
Have you already found a place you liked? I am just not sure about finding car rental agencies there.
San Gimignano doesn't have any car rental agencies, you can find several in nearby Poggibonsi which is where you would get off by train on your way to San Gimignano.
Neither are simple to reach directly from Venice, both will require train changes in Florence at the very least.
My questions are these:
- do you want to rent a car or are looking for a base where you won't have to rent at all?
- how many days total will you be in Tuscany?
If you wish to drive, then getting the car rental in Florence and then driving out to your destination will make it easier to organize. There are several car rental agencies not far from the SMN train station in the center of Florence - make sure to read this:
https://www.visitflorence.com/florence-car-rental/useful-tips-for-car-rental.html
This opens up the possibility of staying anywhere you want in the countryside - for lodging recommendations, take a look at
http://www.tuscanyaccommodation.com
If you don't want to rent at all, either consider Florence as a base or any other town with easy train connection to the rest of Tuscany. I would suggest Montecatini, Pisa, Lucca as good bases from which you can explore many parts of Tuscany by train, with no car.