Hi Cardfan,
Yes, do have your students take prepaid debit cards. They're the way to go. I posted some information about them
here. I've been doing this for a few years. Occasionally a card won't work. A card MUST be activated in the US before use abroad, and we've found that it is best to activate it at an ATM machine, and not online. Online activation is not reliable.
If a kid is using a standard ATM card, connected to a bank account, be sure they call the bank so it can be used abroad and not frozen due to unusual activity.
I would recommend that the kids take some cash (not more than $100) in case a card doesn't work, or they use it up! (They should keep it in a money belt under their clothes.) I have also given loans to kids with a card that doesn't work, and I charge the parents afterwards. No one has abused this, the kids were very careful with expenses, and the parents have been very grateful.
Don't be afraid of the warnings about a card that doesn't work - they usually do, and they are definitely better than any other method of getting euros!
You should have some euros with you on arrival, but the kids can get them there at ATM machines.