You do best to take a debit card and get money out of ATMs as you need it.
Don't be in a position where you rely completely on ATM's though as Italy's ATM system is pretty dated and has a tendency to refuse some cards or the terminal links don't always work. Also worth telling your bank that you are using the card in multiple countries as that can sometimes flag as potential fraud and then will block your card.
We never had issues using an ATM in Italy or any of the other countries we've been to.
We never had a card refused and often one's that do are because people put cards in them which aren't accepted. I watched someone trying to put a Cirrus card into an ATM which had every other logo on the machine except Cirrus and they complained the ATM gave me cash but not them.
If it makes you comfortable - get some cash of the different countries you'll be in before you go (your bank should be able to do this for you for a fee) to have before you get to an ATM in the various countries you visit. Then get cash out of ATMs as you go - and get the maximum amount out at a time you can to cut back on the number of trips to the ATM and any fees you may incur from your bank.
We have used ATMs all over Italy from the most remote village to the largest cities and have never had a problem. Dozens and dozens of transactions over the years.
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