May I chime in here. In Italy in particular and Europe as a whole, any insurance cost from the renter is worth it's weight in an incident or accident.
Whilst ignorant of the cover that Credit Cards offer (we do not enjoy these benefits) let me share with you. Firstly take CDW, Theft protection, and above all pay to have the waiver on the excess damage. Why? Well for a start, driving in Italy is not for the faint of heart. Rules are there to be ignored at best and broken at will. Hire cars stand out a mile and theft is rife of and from the vehicle. From Venice to the borders of Eastern Europe the distance is small. If the other party latches on to the fact that you are not local then matters can get expensive - sorry this is not hearsay and gossip, this is experience.
After I was hit at traffic light by the van behind, I drove the car straight to Linate. All they cared about was which insurance I had. As I had full coverage there was no problem. Furthermore examine the car most carefully, and if you are picking up at night take a small torch or flashlight with you on vacation. Check the car fully. It is the oldest trick in the book to palm a car off with damage, and then get it paid for by you. It may have Avis, Hertz etc on the door, but it may well be a franchise operation and they are trying to offload damage that was not noticed previously.
Make them tell you what the controls do, and whether it runs on petrol or diesel. If you can get a diesel do so as it costs far less in most of Europe, and a bit less in Italy (compared with what you pay in the USA, you will think that you are paying for the lifestyle of a rich sheik each time that you fill the car).
One last thing, and this is not really on topic, but I hope that it is of help. Compared with the rest of Europe (and I make no exceptions in the EU), buying fuel in Italy dates from the 50s. Everywhere charges about the same, but everything is closed between 13-15.30 except on the autostrade. Don't use the machne out of hours, it will eat your money and quite likely clone your card if you use that. Never leave the car less than full (and check that it is full before you leave) or you will think that you have bought the car lock stock and barrel when you see the tank.
In spite of all the above, Italy is drop dead gorgeous,and I hope that you have a super trip all of you.
Whilst I do not wish to alarm anybody, saving on insurance whilst in Europe can be a false economy. I fully understand that insurance can