When we went on an organized tour, they let us know about how much money per day we should bring. For example, for Egypt, they said about $30 per day. Since ATMs are available all over Italy, I would probably not worry about getting out the exact amount and just take out what you need as you need it - starting maybe with $200. Meals in Italy can be expensive, but they can also be cheap (stand-up sandwich bars, going to the grocery store/market to buy food).

Also, check to see if you are supposed to bring tips for a kitty - sometimes they have a tipping kitty that you are supposed to contribute to (so that the guide can tip for the whole group).

also, it is usually suggested to tip your main tour guide/coordinator. Usually the travel company will tell you how much is normal.