When I was unmarried, I was a virgin, and I wanted to marry a virgin. I got the desire to marry a virgin after reading Deuteronomy, and probably from passages like Matthew 19, I Corinthians 6 on two being one flesh. There was one girl, a friend who I could sense a strong connection with that I found attractive that I decided not to pursue anything beyond friendship with partly because I knew she wasn't a virgin. I don't think I broke any hearts. She seemed to show some interest in me, but she was on the rebound and had lots of prospects, so I don't think I broke her heart.
As believers, we should receive all the Lord receives. If someone was a fornicator, adulterer, abuser of himself with mankind, or whatever, but has been washed by the blood of Christ, He is our brother. The same goes for women. But that doesn't mean you have to marry someone whose done those things if you don't want to.
I don't think it's a sin to marry a nonvirgin if she wasn't married before. I have encountered that viewpoint before. Fornication does make two one flesh, but it isn't marriage. If she'd slept with one man and he's a viable marriage candidate (e.g. a believer, not a close relative of hers, not married to someone else) I don't think it is good to get in the middle of that. If I were dating and I were considering single moms, I'd stay away from the situation where the single mom had a child with another single guy. They could end up together, and that might be better for the kids.
Statistically speaking, I've read that women who were either virgins at marriage or only slept with the man they would end up marrying are at a lower risk of divorce. A citation I've read in an academic journal is a study by Teachman. I don't know the year or name of the article. That doesn't mean that someone who sinned in this area is definitely going to get a divorce. But virgins are low-risk.
If I had never married at this age and had the same thoughts, values, and opinions, I'd either be looking for virgins or widows who'd only slept with their husbands. Especially in this society, divorce is so prevalent. I'd look for someone with similar views and similar doctrinal views. They wouldn't have to line up exactly but certain things would need to be the same. I'd look for someone who was anti-divorce. I'd read scenarios on the divorced or married forums on this or other forums or get other examples and ask her opinion. If she gave answers I did not consider in line with the word of God, I'd open the Bible up and discuss it with her (and do that even if she did) and discuss what the passages have to say. If, after all that, she thought it was okay to divorce if you didn't feel 'in love' or if you couldn't get along, or if you couldn't agree on what to do with the money, or if you weren't happy, or whatever, I'd have to take the relationship into the 'just friends' zone.
I'd also see if she had similar views on how husband and wife are to relate to one another. I'd make sure she believed in the husband being the head of the wife and the wife reverencing her husband and submitting to her. I'd ask myself if I could love this woman like Christ loved the church. I'd be looking for someone I fairly easy to love. When your dating, it may be easiest to love, anyway, so I'd think through that. I'd also consider if she would respect me as a husband or be controlling or a nag. That's something you have to manage after marriage somewhat just by how you react and interact with your wife. But you can see how she treats her father if she has a relationship with him, and see how she treats you now. Proverbs warns against a quarrelsome woman.
It may sound a bit old fashioned or Draconian to suggest this, but it is important that a wife be a hard worker. (That's an equally important trait if not more so for women looking for husbands.) Proverbs 31 shows us that the virtuous woman works hard. Her arms are strong for the tasks she does. She has a light going at night. I'm blessed to have a hard-working wife to makes sure the house and kids are taken care of. She cooks great food all the time. I let her handle thing, but when I go to prepare a meal, I realize she puts a lot of effort in planning meals in advance so she can shop. Cooking is a hobby of hers, but it's a lot of work, too. It's a real blessing. Every once in a while on the marriage forums, you read about someone with a lazy spouse who sits around watching TV or playing video games. It's a really important issue for marriage.
As far as marrying a woman with children goes. One the one hand, it can be a good work to raise children who are not your own biologically. There are parents who adopt and take foster children and love them. Some men become step-dads. But if there is another father in the picture, that is a real mess to get into when you don't have to. It's hard to exercise leadership over your home if someone in the home has another father and you are married to the woman he fathered the child with. I know it's common nowadays, but it sure is complicated.
It's easy to think of facts when you aren't involved emotionally in the relationship, like the posters on the forum. If you are spending time with a real life human being, it's a lot different than discussion a list of attributes. Something else to consider is God's will specifically for your life. I was reading an old journal of mine where I wrote down prayers and things like that, and kept a record of some of my conversations with my wife when we started seeing each other. I realized then, I actually checked for a lot of things I advised above. There are a few things I did not go into as much detail as I would advise someone else to know with the benefit of hindsight. But I have been blessed to get the wife I have.
The other 'leg' of my two-legged approach to finding a wife was to pray and get direction from God as to who I should marry. I wanted the Lord to speak to me about it and kept in prayer about it. It seemed like the Lord was telling me she was supposed to be my wife, but I wasn't sure I was hearing. One time, she got upset about something on the phone. Not angry or anything, just our conversation had touched on a sensitive topic. I prayed and sensed the Lord was telling me a story about something that happened in her past and that was why she was upset. The next time we spoke on the phone, she told me that story. Little things like that helped confirm that I was on the right track. There were lots of little things that pushed us in the right direction as we overcame obstacles to getting married. After I had decided to marry her and prayed about it, someone prophesied over us that we would go to many places and minister to many people, which seemed to imply that we would be together for a long time.
With my wife, though, I did not have a really big thing to overcome to make me want to be with her. She hadn't slept around. She was a virgin. She loved God, prayed a lot, no drug abuse, no big red flags, for any of the important criteria I had. Still it was a big decision. In that situation, a quick engagement makes more sense, IMO.
If you don't want to marry this woman, though, and you just know it's not going to happen, don't continue to date her. If you are going to imagine her sleeping around with other guys, and that's going to be a problem for the rest of your life, then you probably should back off of the romantic side of the relationship. She's young but she has a child, so she may want to get married. Dating long eats up time she could be looking for a spouse and it eats up your time. It can also open up more temptation for fornication.
If you don't think she's the right one, but you keep dating, you could end up in a situation where you marry her just because you are too attached or because you've taken up so much of her time you feel guilty, and if those other issues like imagining her with other guys remain, that wouldn't be good.
I say pray about it... a lot. It is possible to get direction on things like this or for the Lord to answer specific prayers that lead you in the right direction like he did for Abraham's servant with Rebecca. You could also spend some time fasting.
