Home base for trips to Florence, Siena, Montepulciano, San Gigminiano, Pienza

Given the high cost of rental cars you'd be well advised to minimize the time you actually need one.
That said, my suggestion would be Siena. You won't need a car to enjoy the beautiful city, and you wouldn't need (or want) one for day trips to Florence which can easily be done via public transportation.
There are several rental car outlets in Siena, including at least a couple near the train station. Renting a car from one of those for a couple of days would allow you to enjoy drives thru the Tuscan countryside at your leisure, including day trips to Montepulciano and Pienza. Cheap parking is available in the underground lot in front of the train station making it pretty simple to get on the road and be on your way. Renting a car for day trips would mean that you wouldn't need to reserve a vehicle large enough for 4 people plus their luggage - just big enough for the 4 adults.
You'll need to study up on Italian rules of the road before getting behind the wheel - particularly the laws dealing with the ZTL's (look it up) that seem to cause so much angst here. And get an International Driving Permit (IDP) for everyone driving.

We are basing in Montecatini, we are also renting a car and first time driving! We plan on only using the car to get to places in Tuscany that are only accessible by car (Pienza, Montecpulciano, wineres etc.). Montecatini has a train station so we will be using trains to get to Florence and Lucca.

There are pitfalls you have to avoid when driving - the major one is the dreaded ZTL - limited traffic zone. Virtually every town, city, village has a historic center that only authorized vehicles are allowed to enter. They are marked by street signs and policed by cameras. Steep fines are assured for each violation (and if you aren't watching out, it's apparently pretty easy to commit). If you are staying at a hotel within the ZTL that has parking, you can get a temporary authorization but probably not until you've checked in. There's also the parking problem. Hill towns generally have parking lots outside the town walls but they can fill up quickly. San Gimignano has limited public parking and my research indicated that if you aren't there first thing in the morning, you are likely to have real difficulty.

My advice is to stay in Florence (terrible city to drive in) and take the bus for day trips to Siena and San Gimignano. Montepulciano and Pienza are about a 2 hour drive from Florence - not really close enough for a day trip. If you're really set on it, find a private tour for 1 or 2 days.