Ralph,
To begin with, your Verizon phone won't work in Italy unless it's one of the "dual technology" models. Verizon & Sprint use CDMA technology, which is not compatible with the GSM used by 85% of the rest of the world.
Two methods you might consider. There are always LOTS of unlocked quad-band GSM phones available on E-Bay (and as with anything on E-Bay, keep in mind "caveat emptor"). You'd probably be fine with just a basic model such as one of the Motorola "flips" or a Nokia (depending on whether you prefer the flip style or bar style).
When you arrive in Italy, purchase a PAYG SIM card, insert it in the phone and you're ready to go. I've seen a few posts here indicating that a Codice Fiscale is required to purchase a SIM card in Italy, but I don't have any specific information on that. Hopefully someone else can clarify that?
You could also just stop at the nearest Cell phone shop (perhaps at the airport?) when you arrive in Italy, and buy a basic PAYG phone. The phone will probably be configured with Menu choices in Italian, but the "sales associate" should be able to assist you in changing that.
They may encourage you to buy a phone with Web or E-mail capabilities. You'll have to decide whether you want to pay for that. You might want to check the web sites for TIM or WIND to see what kind of price plans they offer. Unfortunatelly the sites will probably only be shown in Italian.
Good luck and happy travels!