Before arriving in Milan, make sure you get an International Driving Permit (IDP) from your local AAA office. You'll need this and your regular driver's license to rent a car in Milan. Check the rental company's policies for who's allowed to drive the car, including both age limits and rules about additional drivers, as well as rules about traveling outside Italy.
Insurance coverage for your rental car in Milan is required by Italian law. Usually your policy from the States will not cover rental cars abroad and the same often goes for coverage via credit cards. Check your policies thoroughly and make sure to get all the insurance for your rental car in Milan.
If driving your rental car in Milan is a bit wild at times, then parking is completely crazy. You will be better off with a small car. Make sure to book an automatic if you have never driven stick shift.
In Milan, you can park in spaces marked with blue lines. You'll need a blue parking card available at newspaper stands and tobacco shops. Check off the appropriate spots for date and time, and put the card on your dash. You may find it easier to use a parking garage. If you're driving on the autostrada, or highway, be aware that you'll need to keep your lights on, even during the day. And keep your speed below 130 kilometers per hour or the hidden traffic cameras may zap you with a hefty fine.
Multinational companies like Hertz, Alamo, Avis and Sixt are all located in Milan. You may also want to try Europcar, a large European car rental company as well as budget bookers like Weekrent and EasyCar.