Laura,
Regarding which type of luggage to use, my first question would be what type have you been using so far and are you comfortable with that? Are you planning to go with carry-on luggage only, or check larger items?
My travel method has consisted of a Backpack and companion Daypack (which I use for carry-on) along with a Camera Bag. I'm considering trying the "carry-on only" method on the next trip, using an Air Boss shoulder bag. I'm still not sure I can manage with that, but will probably give it a try.
There are lots here that use the RS Convertible Bag and seemingly very pleased with it. However, whether it's allowed for carry-on will depend on how full it's packed, whether it's "expanded" and of course the weight.
"Adding any additional nights to a escourted tour?"
YES, absolutely! I always add some time either before or after a tour to visit other locations. I'd suggest arriving for the tour a few days early, so thay you have a chance to get over jet lag.
As someone else mentioned, you'll be provided with RS Money Belts. If you feel you wouldn't be comfortable with a "waist style" Belt, have a look at Magellans for neck, belt loop or leg Money Belts.
Regarding credit / ATM cards, I always take at least one credit card and two ATM cards on different accounts. Note that credit cards may not work in automated ticket machines in Europe unless they're the newer "chip & PIN" type. Your travel funds must be in a chequing account with four-digit PIN.
I always take €50-100 cash for expenses during the trip, until I get settled at my first location.
What sort of documents are you planning to copy?
If this is your first trip, you might find it worthwhile to read Europe Through The Back Door, as it will provide you with lots of good information. You'll be provided with the Italy guidebook with your tour package.
Happy travels!