What I looked for those many years ago was someone who treated me well, with a good sense of humor, who was good to other people in his family, too. And I looked for that long before he would have the chance to get close enough to be my "baby's daddy." He was my husband many years before he became the father of my children.
My Hubby isn't our boys biofather, but when we were dating, before he met them, he said something to me I will never forget... He said, "your boys don't have anything to prove to me, I have to prove myself to your boys". That right there made me realize where his priorities were. He loves them unconditionally, and that is what matters most.
Since my husband is the father of our children, I chose a man who was physically fit, a non-smoker, family-oriented, honest, caring, financially secure, had a well-established career, had common interests, likes and dislikes, and didn't have any children from a previous relationship or marriage. My husband looked for the same in me.
How he treats my daughter and me. That would be the most important thing. If he were to want to have a relationship with me, he would have to remember that I am a parent and that always came first before anything else in the world. Their needs would come 2nd. I don't care what they are looking for. I have children and if they couldn't handle it then they don't need to be with me at all.