medical insurance

I would tend to err on the side of what is possible & purchase the personal liability insurance the rental agency offers, as well as opting for full collision coverage.

I've don't recall being offered separate medical insurance by a car rental company. My home medical insurance covers me for emergency treatment anywhere, but some policies have limits such as you cannot be gone from home for more than 3 months. Do double-check your policy. Medical treatment generally does not cost as much in Italy as in the USA, even for visitors. Medical evacuation insurance, to fly you home with medical accommodations, is separate. See also:

http://www.ricksteves.com/travel-tips/trip-planning/travel-insurance

http://www.ricksteves.com/travel-tips/transportation/car-rental-cdw

As Laura suggested, you will want to be careful about this detail, especially if you are over 65.
We don't know the details of "our regular medical insurance." You should have your regular medical insurance company provide you, in writing, of those details.

I work for a medical insurance company and I can tell you some medical insurance packages have a "pay and pursue" policy. This means your medical insurance policy will pay any medical bills that are the result of the accident and then will settle with the auto insurance carrier (either yours or the other driver's depending on who is at fault) on the back end. You'll want to call your medical insurance provider and have them provide you (in writing) the terms of their coverage in the case of a driving accident as these should be spelled out very clearly. They should be able to send you a copy of your policy's coverage via letter or in a digital format (pdf).