I don't think age has anything to do with whether or not someone is "classy" or "trashy". It's the behavior that will get kids labeled. Kids know who the "fast" ones are, or the ones who have no supervision.
A 13/14 year old girl who has a boyfriend or is "going out", (and I'm not talking about a guy picking her up and actually going somewhere), and who has a lot of parental supervision and involvement, and open communication with parents, is going to be a heck of a lot better off than a 16/17 year old girl who has just been allowed to date, and has little or no parental involvement.
Every parent has the right to set whatever boundaries they feel are appropriate for their children. I don't think there is one magical age for dating, though. I believe it should depend on the teen's level of maturity, trustworthiness, and level of responsibility, and on the ability of parents to stay connected to their teens and know where they are and what they are doing.
Communicate, communicate, communicate!