Well, it's
Hmm. Well let me try and address your points one at a time, as briefly as I can.
1) Because there are plenty of quality women in the world that don't deserve to be passed over just because they have made a few mistakes. Not everyone will have shared your journey or your perceptions, but the mistakes they made and the experiences they had make up who they are today. I also believe that while as virgins, we certainly have a right to be picky, it ultimately isn't beneficial to be picky, for the reasons I said.
2) I'd draw on the fact that they love me now, and that I love them and am attempting to build a life with them. You can either ask that she disclose who she was involved with, or you can just elect to never bring it up. Being that it's generally a good idea to get an STI test done, the issue will come up sooner rather than later.
3) Basically someone who wasn't willing to be patient and wait. While I'm not opposed to women who have had multiple partners, I wouldn't want a woman who has a reputation for sleeping around. Also, while I am comfortable with the idea of dating a single mother, there's limits, and mine is no more than two children. However, when dating a single mom, you have to be patient and understanding with her, because her time is not really her own, and ultimately, you are not a priority. So you'll have to mature fast and just be patient.
Anyway, hope this helps. If you have any questions, tag me, and I'll respond.