If you intend to take a ferry to Positano, it might be best if you take a high speed train Frecciarossa from Roma Termini to Salerno, then take a ferry to Positano. I think it's faster (the ferry in Salerno is walking distance from the station, and there are more ferries to Salerno). Salerno is the next high speed train stop after Naples.
The best choices are (in order of driving distance from Positano):
Sorrento
Salerno
Orvieto (Hertz only)
Chiusi (Avis-Budget only)
there are only two choices: in the city center near the station (exact location varies depending on rental car) or airport (requires a 20 min taxi ride to your hotel for approx 25€ or a tramway ride from the airport terminal to the SMN central station for a little less than 2€ per person). Returning to the city center has challenges due to ZTL traffic restrictions, refer to some of my previous posts for directions (use the search function above).
To rent a car I use a broker called www.autoeurope.com.
They do not work with the Orvieto Hertz franchise office I think due to poor customer service
In your shoes I would probably rent a car in either Sorrento or Salerno and drive the 5 hour (mostly freeway) to S.Casciano dei Bagni. From Salerno is faster since you get immediately on the freeway (just over 4 hours). If you want to minimize driving then Orvieto or Chiusi are best, however it will require multiple train changes and you will be dealing with small franchise offices, therefore they will be closed at lunch time for a few hours, they will close on Saturday afternoon, and all day Sunday. That is probably true in Sorrento as well. Both Sorrento and Salerno have offices with the major rental companies, while Orvieto only has Hertz and Chiusi only has Avis-Budget, both are close to their respective train stations. If those offices don't work for you, then Naples has plenty of choices, but I recommend to rent from the airport because driving out of the city center is a nightmare. (I still recommend picking up the rental in Salerno).
Edit: If you plan to stay in Siena be aware that Siena also has a ZTL (Limited Traffic Zone) where cars are prohibited except for residents with permit (violations are enforced by camera). Therefore you must choose accommodations outside the ZTL, or park outside the ZTL and walk to your accommodations. The Siena ZTL encompasses the entire historical center.
2nd Edit: I checked www.autoeurope.com for rental rates for a random week next month, with pickup at Salerno or Sorrento or Chiusi (AutoEurope does not work with Orvieto Hertz) and return at Florence a week later. The best weekly rate is with pick up at Salerno, the highest is the one with pick up at Chiusi. It is probably because Chiusi Avis/Budget is the only game in town.