Hello Silvia,
If you really want to see many small towns in Tuscany renting a car is probably a necessity. May of the smaller towns are not well served by public transportation so it is harder to visit many of them without a car. You might look and see what you're interested in and maybe do a "train" half of your trip - Lucca, Pisa, Siena, Arezzo are all reasonable by train and then a car half where places like Pienza, Volterra, Montepulciano and Montalcino are on the plan.
I would suggest choosing two or three bases and exploring the area around each one. Search the many "best towns in Tuscany" guides and decide what your tolerance for daily driving is and see what's close enough to string together several cities and choose some bases at which to stay. I spent a week outside Castellina in Chianti which is between Siena, San Gimignano and Florence and many smaller towns were within reach for this area. If you really want nonstop small Tuscan towns I would suggest one more northern and one more southern.
If you plan to rent a car brush up on ZTLs and when approaching towns take the suggested "Park Here" outside the towns and don't assume you'll do better closer to or inside the town. And get an international drivers license.
Pisa and Florence are the closest airports but Rome and Milan - the big international ones - can work just leave some time on the ends for airport logistics. You can rent a car many places but popular choices are from the Florence airport (just outside the city) or from Orvieto or Chuisi training up from Rome in the south.
Check on festivals and sagras that might happening and plan accordingly. Also be sure to schedule enough down time and get into the easy flow of Tuscan countryside life. It is as beautiful as advertised so be sure you're soaking it in and not scheduling every day.
Have an amazing trip,
=Tod