From what I have heard, the teens mostly like the signature fabrics. More obvious that you are carrying a designer purse if it is a signature fabric than if it is a more subtle leather one. I bought a Hampton wristlet for my niece with the signature fabric and the gold leather trim. The SA told me that the teens all really like the gold leather trims because it adds a little bling without being too over the top.
Definately go with something small. At 13, she doesn't need to carry too much because, hopefully, she doesn't have credit cards or a check book. So she wouldn't need a full size wallet. But a smaller purse with a wristlet should be fine. Heck, my Mom who is 68, carries all her stuff in a small wristlet that I bought her.