Before I moved overseas years ago, I signed up for a CapitolOne Mastercard. This card has NO foreign exchange fees. Being a large group, it also gets some of the BEST exchange rates! In addition, they have a pretty good fraud department (which has actually worked against me!).
Unfortunately, I have a Bank of America debit card (still) and they charge $5 for every withdrawal... and although you can get free withdrawals in France and England at specific banks... they DO NOT have any agreements with Italian banks. Thus, I rarely use it. Thankfully I have Italian and Danish debit cards and I use those. So, as suggested, see if your bank(s) have any agreements with Italian banks. ATM's are the BEST way to get money (and at the best rates) in Italy.
Read this for more info on Italian ATM's.
I have a Platinum AMEX card and I rarely use it in Europe. First, most vendors do not want to see it. They'd rather you use a VISA or MC as AMEX charges them excessive charges. And AMEX will probably charge you 3%! You will see locations that only take VISA or MC.
Forget about Travelers Checks. Most vendors will not accept them and in order to cash them you have to go to a bank... and then the bank charges you a fee to cash the travelers check. You don't want to bring traveler's checks to Europe anymore.