Are you an Italian citizen? If not you can't buy a car in Italy unless you know someone who could buy it in there name. Having said that unless you have a garage on your property the only parking is in the streets ( no room) or in the square (town might object) or you might find someone in the village with a garage they would rent.
As we only go for a month at a time we just rent a car.
I haven't checked it out yet but some of the french car makers offer short term leases ( 1 to 6 months) that are supposed to be quite good. If we were staying more than a couple of months a year then leasing a car might make sense. We have a garage (for now) so have a place to park it.