Just to remind people, the money belt is not instead of a wallet. It is for "deep storage." You keep things in it that you do not expect to need during the day. If you spontaneously decide to make a big purchase, you can go to a back room or a toilet to take out your credit card or a big wad of cash. If you need to make an ATM withdrawal, do it when you leave your hotel, then find a private place to put the spare cash and the ATM card back in the money belt.
I often wear a money belt through airport security. As long as it is under your clothes and doesn't set off the metal detector (do not put coins in it), you'll be fine.
I find the neck pouch an annoyance on the back of my neck and generally uncomfortable. I sometimes use one only for flying. I wear it over my clothes, undoubtedly look dorky, but I know exactly where my passport, boarding pass, and credit cards are. I know that I'll need the passport at both ends of the flight and again when I check in at the hotel, so it's convenient.
I've used several money belts over the years. My favorite is the Rick Steves one. It's flexible, lightweight, and comfortable. You won't want anything synthetic in Italy's heat. An elastic band makes it easier to slip on and off without using the buckle.