When I was younger, I was a big proponent of simply accepting the woman for who she appeared to be and not getting hung up on her "past" per se. If she and I appeared to jive then I wasn't going to worry about it in deciding whether she was LTR material.
I can tell you I have completely changed over the course of the last decade. Through a few bad experiences in LTRs, I can tell you the history of the woman is extremely important if/when you are deciding whether she is an LTR material. Certainly, the obvious ones of her dating experience/how many men she has slept with is relevant and is probably the most focus guys here at SS will mention to you. However, what is even more important IMO is her childhood experiences -- primarily those with her parents and moreso her father. Alcoholism, physical/sexual abuse, co-dependence, completely absent father, etc. all are festering experiences that leave scars -- sometimes wounds that are never going to fully heal in the woman's psyche. Trust me that you will be dealing with them over the course of years and sometimes even months and the psychological problems/personality defects they cause will be hugely problematic.
Obviously, this isn't information you can get on a first date (unless she is really crazy lol), but do your due diligence before you dive head first into an LTR (and certainly before you move her in or think she is wife material!).