Rented one for the first time this Sept and driving and the rental process is not hard. Make sure to read up about ZTL zones, go to AAA to get your DL from the states translated into an Internal Drivers Permit.
Ok to do just for your DH if he will be the sole driver. It adds a daily fee to have more than 1 driver anyway.
I used and would recommend Autoeurope.com
I would look at the site for the options and then call so you are somewhat knowledgable first rather than blindly calling, they are a consolidator so sell different brands, stick with something from Europcar, Hertz or Avis ; avoid the others. We used Europcar and had a positive experience.
You will get a manual unless you pay a good amount extra and insist on an automatic.
Keep in mind small cars in Italy are much smaller than small cars in the US. What they consider mid size or intermediate you likely will think is a compact, it will just be a better grade of car rather than a physically larger car in many cases. For comfort reasons you might not want to go with the lowest cost option and also look at the luggage space.
Usually best to rent from a larger city where there is competion, for your trip I would rent as you are leaving Florence right before or after check out. We used the Florence city office of Europcar for pickup and it was painless. We had stayed in Florence and when leaving town went to the office and drove out of town just follow their instructions on getting out without going into any ZTL zones. It will be fairly straight forward.
There are a couple of Florence offices, this is the one we used and was good for driving out of town plus a short walk from the train station area and most attractions in Florence.
Via Borgognissanti, 55/red
The countryside you do need a car to explore properly, some of the roads can be narrow and curvy so you need to pay attention at all times but driving around is not a problem.