Normally I don't think parents should share too much of the details with a teen, especially if they were very sexually active or did a lot of recreational drug use. I don't think it's a question of lying, but of sharing info when they are too young to really see it in perspective. I don't think it's necessary to be super open about everything just because a child or a teen asks.
But in your case, you married very young (19). You didn't have a whole huge number of partners, and you do regret the early experiences. You say that she sees you as "straight laced" and, what? You think she will think you have nothing in common with her, that you can't possibly understand? It's important to let her know that you appearing "straight laced" (as if that's a huge negative) is a choice you made.
I think it's really important that you convey the feelings you had about being "lucky to even have the boys like you" and the pressure to use your body (and give your body) as a sort of offering to them, a payment for keeping you in their esteem. I think you can communicate that whether you answer the "sex or no sex" question directly or not. If you normally have a very frank relationship with your daughter, it might be okay to tell her that you had sex at 15. She needs to know there's a strong sense of regret and of feeling worse afterwards. The risk is, she'll think you turned out okay and so it's no big deal if she does it at 16.
If talking about regret would be "too heavy" for her, then she's not ready for a sexual relationship. I think there are lots of factors in whether you tell someone your sexual history, and I can't really offer a firm opinion one way or the other without know you both. I think there are risks, that's all. I think you can consider raising the issue of privacy for her - that she will see all kinds of kids bragging about their sexual exploits and history and think it's okay to discuss all of this publicly. You can say you consider it private, but that you do look back on the pressures you felt with some dismay.
I think you can also raise the topic that what you want for her is one thing, and what she will do may be the same or it may be something else. But she needs to know about contraception and disease prevention from reliable medical professionals and counselors, not from "the street" or her friends or the internet, and certainly not from boys. She needs to know that the responsibility for protecting herself comes first, and the sex second. Someone who's not mature enough to see and do that is definitely not prepared for the realities of sexual activity.