This last trip in 2013 i spent around $100 a day minimum for myself in Italia. Oddly a couple I know also spend $100 a day for two!
Yes, buy Euro here at home. I have enough Euro on me for food, some good stiff drinks, caffe', taxis, and several days' living so I have time to settle in, run around, freak out, and then think about finding an ATM inside a bank alcove.
Your local bank will use money from your account with them to buy the Euro. Your bank will explain that process.
Yes, you can exchange US dollars for Euro here in the US, but first ask your bank to recommend a reputable company that will exchange the cash. If none, then deposit the cash in your account if you are happy with your bank's procedure for buying Euro with money from your account.
Otherwise, you can exchange US dollars for Euro at Poste Italiane, the Italian Post Office, the very best place for this. Remember you will have to show your Passport before the exchange. I paid the same conversion rate at Poste Italiane that I paid at bank ATMs in Italy and paid here in the US for cash exchange. I'm referring to the amount of dollars it takes to make one Euro.
As for fees, i used two different Debit cards from the same bank here in the US at Italian bank ATMs. One Debit card charged a $5 fee for every withdrawal. The other Debit card charged No fee.
You said you already know the fee for using your debit card in Italia? Well be sure to ask your bank about fees attached to using your Credit Card for all your international purchases and services you want to make.
The only time I used a Credit Card in Italia was to reserve a room, and then I paid for the room with Euro cash so my Credit card was never charged. I did rely on obtaining Euro from bank ATMs with my Debit cards.
I meant to say 100 Euro Minimum. Actual range i spent on myself in Italia last year was 100 Euro to 150 Euro each day.