Euro

I travel a lot so I generally have euros left over; so I only get cash from an ATM while over there.

However for the new traveler I recommend 200 to start small bills; conserve that cash by charging everything where ever possible.

When the cash is running out only use ATM'S attached to a local bank when it is open.

If you are not accustomed to traveling to popular tourist destinations domestic and abroad, it is a good idea to carry excess cash under your shirt in pouch and not in a wallet in a back or front pants pocket.

Your costs will be any lunch and dinners not covered, any extra side trips you take during your free time and any general spending money you want for souvenirs. Perhaps a small amount for laundry services.

You can charge most of these expenses. If you want to pay cash, you have 2 options. Bring Euros as your question states, or do periodic withdrawals from ATM machines once you get to Italy itself.

Most members of this forum would recommend the ATM approach.

Master traveler Rick Steves FAQ suggestion: https://www.ricksteves.com/travel-tips/money/cash-tips

Resist the urge to buy foreign currency before your trip. Some
tourists feel like they just have to have euros or British pounds in
their pockets when they step off the airplane, but they pay the price
in bad stateside exchange rates. Wait until you arrive to withdraw
money. I've yet to see a European airport that didn't have plenty of
ATMs.

While I agree with Rick, a number of forum contributors feel more comfortable with 100 or 200 EUR in hand before arrival.

PS Euro cash strategy depends in part on your financial institution's fees and exchange rate/premium. Our debit cards do not charge fees other than a 1% FX transaction for my credit union account and 0% for my wife's Schwab debit card. Some major banks charge as much as $5 US per transaction and up to 3% above Inter bank wholesale.