You have received good advice from the female solo travelers posting. I, too, am often a solo female traveler, in my 60's. Credit cards are so much more encouraged these days by many countries and with no transaction fees, I find I need less and less cash with me. I feel more secure just using a credit card (with another or two for back up). However, I haven't been to Italy in the last few years so others will need to say how successful the card users are there. Some people just insist on using cash, which is fine, but I'd rather save mine in case of an emergency.
If you don't use your ATM card at home, you might find your bank has cancelled yours. So do take others' advice and make sure it is working at home a few weeks in advance of your trip so you have time for them to send you a new card should they have cancelled it. I've learned to use mine for 10.00 dollars here and there just to keep it active.
This being said, I always start out with the local money from home, $200.00-300.00. My local AAA office seems reasonable. I guess AAA rates vary per region, but worth it regardless, IMO. (People will argue against this, but to me it is worth another few dollars for the security of already having it and taking my time picking my ATM.) It also lets me become familiar with the different bills, particularly if they are not Euros or Pounds. Lately, I've found with this amount of pre-trip money, I'm spending it during the last days of my trip because I haven't needed it. (Or in the case of Sweden, I spent little of it and paid cash to the airport for my trip home to get rid of it.) More important, by bringing cash with me, I have a few days to choose my ATM. I've never found one inside a bank...might be my lack of observation, but whatever. What I do is ask at the reception desk of my hotel where I can find a safe, reliable ATM. I've never been scoffed at, but rather they will send me to a specific ATM saying it is secure and very busy. I'll stuff my card and money into my pocket or purse and go back to the hotel to organize.
I've only been in Naples for a limited time and I can't wait to go back for a few days. However, if Naples is at the end of your trip, I would have money before arriving there, but there are solo women travelers who have been there and needed money who will hopefully chirp in here. Otherwise, IM Chani as it seems to me she's spent time in Naples. I think it is mainly having a system and keeping money/financial separated. In all my trips through the years, money belt or not, I have never had a pickpocket problem. Look confident whether you feel it or not. And ask your hotel for recommendations.
You'll have a great trip. Traveling solo is great fun and you meet many people throughout the day. I've never felt a threat from pickpockets and never had an issue, but keep the items you are not using each day in a harder to reach spot than your daily cash or daily credit card...no worries, really. Pick pockets are rather overblown on this site unless you tend to leave your purse not attached to you in a restaurant, open, or walk away from it; ie, in a shopping cart in a grocery store (drives me nuts). Common sense works wonders. LOL. Have a wonderful trip and if you get momentarily nervous, just take a deep breath, compose, and move on.