Advice: Do Not Give Your Kids a Visa or Mastercard for Travel, Give Them An Amex
I am a flaming hypocrite on this topic, because my company does not accept Amex, but for travel, particularly if it is a shared family card you are giving your kids, don't use Visa or Mastercard. Most banks have systems now that are simply hair-trigger in freezing an account if they see a charge they don't expect, which generally means a charge in a new city, ie when you are travelling. It is merely irritating on my own card, as I have to call and get it turned back on (which can be a pain in certain foreign lands) but it creates a real problem for my kids. Twice my son has been travelling and twice they have immediately shut down his card. When he called, they would not talk to him so he had to find me somewhere and I had to call them to verify a charge. But since I did not make the charge I have to call my son back and then call the credit card company back. All the while my kids are without any way to charge because this likely is their only card.
There are things you can try to do to avoid this, such as remember to contact the card issuer to warn them when you will be out of town, but this only has mixed success and trying to have my kids remember to do this is a tough proposition. In my experience, perhaps due to their background as a travel company, Amex is far, far less likely to have travel to new lands trigger these sort of pre-emptive account shutdowns.
Postscript: I don't get a commission, but I have the Starwood Hotels Amex. One Starwood point per dollar spend on the card is a great deal. Starwood points are very valuable, as loyalty points go. Now that they are merged with Marriott, they can be traded 1 starwood point for 3 amex points. Also, they can be exchanged for most airline points for 1 starwood point to 1.25 airline points.