teen travel in Italy

Easiest; just add international calling and texts to your current phone. My colleagues' high school and college kids are often overseas. This is the method most commonly used. Make sure that friends do not call the phone from USA.
Cheapest; Skype. This is also used in combination to decrease the cost of calls. Buying a sim once there gives them a local number to use. You can bring an unlocked phone from the USA and just get a sim. Once you get the sim, they can turn off the USA phone.

The "easiest" method the previous poster suggests will only work if your current phone is a quad-band GSM phone (world phone). And there is really no way to prevent her friends from calling her while she is abroad, since it would use the regular number. The best method (and probably cheapest) would be for her to buy a pay as you go phone when she arrives. Local calls will be cheap, you can add minutes anytime, and calls home won't be expensive, either (though not as cheap as Skype). Better to use a debit card or cash for purchases? Cash, definitely. Use your debit card to get cash from ATMs.

If she does not have a gsm phone unlocked already, just buy one on Craigslist before going. Then when she arrives there, walk into a phone store and buy a sim. They are easy to activate. If she will be working there, someone can translate for her to activate properly. I would not get the phone there with a gap between home and arrival. With cell phones now, pay phones are nearly impossible to find anywhere in developed country. Way back when, when we traveled as teenagers, we called mom and dad collect on the pay phones. No such thing now. For parents, the most anxious time for a teenager traveling alone is the transit time. My colleague had one daughter in india and another in england this summer. She was in constant communication with both during their travels. If your daughter carries a phone with her with international plan activated, she can text and call you at the airports while changing flights and arriving etc. you would not be asking any less of her if she was going to another city in the USA alone. I would get the phone working for the transit time.......

Not everyone has a GSM phone with an international plan available for use during transit time (personally, I wouldn't want to commit to an international plan just for the purpose of having a phone available until I can activate a different phone). Buying an unlocked phone here (and buying the SIM on arrival) is no different than buying a phone with SIM on arrival. You won't know the number in advance of purchasing the SIM, and the phone won't work without one. But buying a supposedly unlocked phone from Craigslist is riskier than buying a brand new phone on arrival because you won't know until arrival if it works.

Just remember to alert you daughter's bank about overseas use of her debit card and to make sure she has a numeric pin instead of letters. I saw a US teenager last summer who's ATM card had been frozen. Fortunately, her fellow travelers were loaning her cash until she could get to a phone to call her bank.

My tip is: buy an unlocked GSM phone in US, then buy a SIM card with an international calling plan. Italy has many pre-paid plans that allow you cheap international calling for less than € 0.25/minute. Is she's staying there for a month, she'll want a local (Italian) number anyway.