We went to Italy last month. I brought extra paper copies of our passports, because I'd heard to use them for ID. We never did, but it was the TA's recommendation. We also left copies at home with DH. In addition, we brought extra passport photos. Plus a letter for my minor DD, saying that her dad knew she was traveling abroad with her mother (didn't need that either).
I have to say, I prefer having everything on paper. OTOH, DD22 is very comfortable having everything on her phone. Maybe I'm just an old fogie?
All three of us used cross-body bags for the trip. Normally I carry a purse, but we felt this was safer. I got ones that were RFID protected and had a zipper lock, along with other safety features. DD22 had the identical bag (different color), while DD14 had a hot-pink leather cross-body that I got in the thrift store for $1.50. DD14 wasn't going to be carrying much more than a few euro, so less protection was needed. I also brought a money belt, but never used it. I only carried enough cash for the day at any given time.
I brought a credit card on the trip, but it's not one I typically use. That was so, if it got lost or stolen, it wouldn't mess up my automatic things, online paying, etc.--I would just have to cancel that one, rarely-used card. I called them and my regular bank before I left, letting them know of my travel plans (I also had my debit card with me). Keep in mind, if you make an ATM withdrawal in Europe, it'll be in euros (naturally). If your daily ATM limit is $300, you can only get 250 euros a day.