I would agree with basing somewhere on the Amalfi or Sorrentine coasts which are served by ferry; you're going to want to use them. I wouldn't choose Capri for 4 nights simply because it's not a great base for exploring elsewhere; you stay there if planning to stay put. I'm also not a fan of Positano due to expense, the many, many steps involved to get much of anywhere, and lack of things to do. Look at Sorrento, Salerno (although Capri is a really long ferry ride from there) or Amalfi. Sorrento and Salerno are also served by rail from Naples (and to/from Pompeii) of one sort or another.
A car on the coast during high season has been roundly discouraged due to very dense traffic and limited parking. As well, during the busiest seasons they've been limiting the days you can drive a rental car according to even-odd numbers on the license plate:
https://distrettocostadamalfi.it/wp-content/uploads/2023/04/Distretto-Turistico-Costa-dAmalfi-Traffic-Regulation-in-Amalfi-Coast.pdf
So the more options you have for getting around via public transit - ferries, SITA buses (which are very busy) and rail - the better. With a group your size, if may also be worth the price of hiring a driver for a day trip.
If you are flying home from Rome, you'll want to be IN Rome the night before your flight. Tuscany is too far away. So you're not planning on spending any time in Rome?
And one more note regarding a vehicle: do your homework about driving in Italy if you've not done so. While a vehicle can be a plus in the Tuscan countryside, you cannot drive it just any old place, such as into historic city centers. Download the free "Driving in Italy" guide linked in the website below (scroll way down the page) to read up on ZTLs, traffic signs, speed cameras, etc. You also don't want to leave anything you can't afford to lose in an unattended vehicle.
https://italybeyondtheobvious.com
