My 15 yr old started with MySpace and most all of the teens are now on FB.
Our "rule" is that I have her signin and password and I check it randomly but frequently. There are some kids who amaze me and have videos, too many pics, etc on their page. Some parents obviously do not monitor their kids's FB account.
I have a FB account and I am active on it. I am not friends with my daughter on our accounts. I simply check her account frequently. We've had no issues.
One thing I did was go to some pictures and show her NOT TELL HER BUT SHOW her how anyone can click on a pic or video, save as and then BAM, they have her pic, video or whatever she has posted. She does have her FB page with heavy privacy settings.
Just do what is right for you and your family. Some people don't let kids use computers at all. Our daughter has her own laptop and internet acces via her IPhone. She does a lot of homework with her computer as well.
Best wishes to making an informed decision.