Obviously there are many options for renting a car in Italy, we have had some good and some very bad. Again it is totally your option we have found two we would suggest you look into. Auto Europe, Cheap Cars. both which are broker websites that will give you a variety to choose from.
If you fly into Venice you will not need the car until you return from the island and then you will pick up your car in the building between the water taxi and the airport terminal.
If you fly into Rome you will take the tram inside the terminal to get you to the rental car terminal, as well when you return the car you will take the team back to the departure terminal. Look for the company name on the sign of which building with letters A-E for the rental return, it was confusing to us.
When you rent the car there are many options and navigation is one of them you should highly consider or use your smart phone or other device, because the offramps off the highway are many miles apart and it you miss the turn you will have an extra long journey. Also if you have a credit card that pays the $1000 damage waiver for you then you do not need to purchase that option, be sure and check with your credit card company first.
Your US drivers license is good for the rental purposes here. Be prepared to show that and your passport to the rental agency. Sometimes they ask for a printed copy of your purchase voucher but usually they don't, you can just give them your name and they will find your booking. You should also purchase in the US before you leave the international drivers license, it doesn't really mean anything but sometimes they request it.
As far as what kind of car to get of course that first depends on the amount of passangers. All the highways are very well maintained in Italy and be prepared to pay a few tolls on the main highways. Usually they take coins only but some will take credit cards. If you are coming during winter months all the rental cars come with sets of chains in case of snow, be sure and ask especially if you are planning to go skiing or up the mountains during winter would you need a 4 wheel drive. Just keep in mind when selecting your vehicle that all the villages and hamlets have small narrow roads and alleys so the smaller then better but don't forget to include space for your luggage.
Detailed driving directions with navigation coordinates will be sent to you the week before you arrive because if you use google maps as your guide you will get lost. Be sure and let us know your atticipated arrival time once you have your flights arranged.