Don't take US dollars with you, the exchange will be costly. Use the ATM/bancomat.
You have a little work to do before your trip. Call your bank to ask them what they charge to withdraw cash in Europe. (e.g My Cr.Union uses the official--is that the word?-- exchange rate plus 1% service charge.) Give yourself time to look around for another bank/credit union if your bank's fees are too high. Make sure you have a 4-number pin & money is in checking acct.
You also need to call all your credit card companies to find out what they charge and leave the bad cards at home. You need time to apply for a new one if yours aren't suitable. Try to get 1 or 2%, no more than 3% plus good exchange rate. You need a back-up CC in your money belt incase your primary card --or even just the number-- is stolen. A second bank acct. ATM card would be a good idea too.
Italy is a cash economy, you don't pull out the CC for everything. I paid for some meals with my credit card, but I never assume. I had to pay for some lodging with cash (an apartment for a week!) but used CC for others because I always had long stays. I would pay cash for one night stays if possible. Italy is also the "land of no change" so carry small bills and ask before using a large bill for small puchases--don't assume. They appreciate it. Sometimes people will tell you their credit card scanner is not working-- it's because they want to get you to pay cash. Keep your money belt stocked so you're not in a pinch.
You should buy "RS Italy" and maybe "Europe thru' the Back Door" and read about money, bank fees, etc. and make a pre-trip checklist, learn about slow count, and about a dozen more! (good prices on amazon.com)
Search this board for lots and lots of other threads on the topic. Also visit this link http://slowtalk.com/groupee/forums/a/tpc/f/559601885/m/74310692311 for more info than you ever wanted to know about cash, ATMs, credit/debit cards etc!
PS I don't recommend taking a debit card