Toscana

Renting a car will provide you with the most flexibility to explore Tuscan villages. There are several places you can reach by train, by bus or by some combination thereof, but efficiency suffers. For example, going from Volterra to San Gimignano is a relatively short drive but going by bus takes much longer and requires multiple changes.

You can easily move along the Amalfi Coast using either bus or ferry. Ferries might not stop in Fiordo di Furore, but you can reach it by bus from either Positano or Amalfi. Capri can be reached by ferry from Naples, Sorrento or Positano.

Before you decide to rent a car in Italy do your due diligence and research it very carefully. Some of the items to search for here and other forums are:

Traffic Cameras Italy
Italian ZTLs (traffic zones)
Traffic Tickets in Italy
International Driving Permits

The short story (but this DOES NOT take the place of careful and thorough research).

Italy loves instantaneous and average speed cameras and doesn't hesitate to ticket people.

Many Italian cities and towns have traffic zones (ZTLs) enforced by cameras and they don't accept excuses from unprepared tourists.

In addition to the traffic/ZTL fine, the rental car company will charge an administrative fee EACH TIME the local officials request information regarding the car renter. There are posting in this forum of people returning to find hundreds/thousands of dollars in credit card charges showing up 6-12 months after driving in Italy.

Finally, Italian law requires drivers from outside the EU carry an International Driving Permit. This can only be acquired in your country of residence BEFORE you arrive Italy (get two passport photos and head to the nearest AAA office with your checkbook). No matter how stupid is sounds, it is their law and there's no fighting it.

As for the Amalfi coast, do a search for ferry and bus schedules. October is the tail end of the tourist season and buses/ferries may be reducing or curtailing service. If the schedules are robust for the duration of your trip, you may not need a car...

You might find it helpful to peruse this thread.....

https://community.ricksteves.com/travel-forum/italy/driving-in-tuscany-3386ca08-f031-4bc9-a3d5-2a1fb58c2408

It would help to have some idea which "beautiful villages of Tuscany" you plan on visiting, as some may be served by good public transit. I would not suggest driving in Napoli, as it's not for the faint-of-heart. Parking could be an issue in Positano and of course a car is useless for Capri.

Florence to Pisa is on the train lines and no car needed. In fact, visiting towns along that route is best done by train. Prato is the starting town, then to Pistoia, Montecatini Terme, and Montecatini Alto (great little spot for lunch), then to Lucca, then a choice of north to 5 Terre, or south to Pisa. This easy to write and a little more difficult to do, but it is doable.

If you want to go down into the heart of Tuscany then you need a car and a nav system, or map.

Moving through the Amalfi Coast is more difficult. Why not stay in one place, take public transport, and day trip the others, and don't forget Ravello.