Here is the best answer I can give you. First, I am the product of divorce. It was pretty damaging emotionally to have step-fathers (more than one) through out my child hood.
Second, if you are wanting to date a single mother, I would ask why? Are there no other single girls in the pool around you?
I dated two single mothers when I was younger. I didn't have kids and had never been married. I would say that it is a very difficult road to travel just to get into a girl's pants. And their are plenty of women out there with less baggage. You also should consider your responsibility as a male role model in that child's life. Whether you like that or not. A child is innocent and can not help the situation they are being raised in.
In both instances, despite my best effort to avoid it, the single mothers used their sons to inadvertently vet me. That never sat well with me. I felt it wasn't fair to those children to have them get to know me if the relationship wasn't going to last and become something solid and permanent (marriage perhaps) in the future.
We all make bad decisions in life. Some worse than others. But in my experience of dating and with observing certain members of my own family, most people do not break bad cycles or bad decision making patterns. It takes a lot of effort and will power. You need to be looking for someone that is your equal. What I mean by that is, if you are a single father then a single mother might be a perfectly healthy and rewarding relationship. You both are in the same circumstances and understand the challenges of it. You might be able to integrate your families down the road as well. So IMHO, you need to be looking for someone that is on the same path as you. Equal footing. Put that goal above all else and you may find the right woman to be your co-pilot.
Luckily, I met my wife after dating a lot of the wrong girls and for the wrong reasons. We have wonderful kids and a pretty good life. I had a lot more baggage than my wife to be sure, but we have been able to weather every storm and do our best to raise healthy and well adjusted kids.