Will the old magnetic stripe debit card work in bank ATM's or do the Italian machines require chip technology?
Magnetic works at ATM machines.
Mag stripes work just fine. Make sure your card issuer knows where and when you are going.
Also, make sure you have more than one card, in case the machine eats one. We carry 3, and a credit card (probably overkill, I know).
The magnetic cards will work. Try to withdraw cash during banking hours, in case something goes wrong (although it very seldom does).