I am a technology consultant and have accounts with twitter, facebook, myspace, etc. In my humble opinion, I would say that facebook tends to be a little more "classy", but then again it all depends on the user and who they are "friends" with. My suggestion to you would be to do the following:
1. Make sure his/her site is set to private, meaning only their "friends" can see her information
2. Set up an account yourself and make sure he/she makes you a "friend" so that you can see the activity on the site.
3. Set some ground rules on what is/is not acceptable; talk to him/her about the importance of not be-friending people she doesn't know.
4. You must be 13 to have an account with facebook - those are facebook's rules.
I think someone else posted this, but I can tell you from experience that employers do look at people's pages before hiring someone. They do it all the time. When we were kids, our parents had the "don't put anything in writing that you would not want the whole world to read" talk with us in regards to note-writing. It's the same thing with these sites! You just need to have that same talk with your daughter. If she is honest and trustworthy, then you won't have any problems.
I think it is also important to stress that you should do this with him/her. Kids these days are using social networking and incorporating technology in their lives at a rapid pace. Whether we like it or not, it has become wildly popular as a means of communication for this generation. By the time your son or daughter reaches college, she needs to have experience using social networking, IM, texting, email, etc. because many of her college professors use these means of communication with their students nowadays. Also, if you allow him/her to set up accounts, but you don't, you are missing out on a very valuable way of staying in communication with him/her. I think if you learn alongside him/her, you will find that you like it. Hope this helps you!