I selected "shit face", but I do want to add the caveat that I think it can be a bit reductive, even if it's true. I do think that finding a relationship is more complicated than just how physically attractive one is, but with the note that if someone is attractive enough, nothing else really matters.
So as an example, if you take a man who is extroverted, ambitious, has cool hobbies, a broad circle of friends, a good job, etc., then he's probably going to do fine unless he looks like a burn victim or has some severe facial deformity. Even in the latter case, there's probably going to be some few women who can look past it.
Whereas if you take a man who is introverted, not particularly ambitious, who doesn't have any notable talents or skills, few to no friends, crappy job, he isn't going to do well on the dating market. UNLESS he is also extremely good looking, tall, etc.
So bearing that in mind - in the first example, the man's attractiveness isn't as important, since he just fits in with society so damn well. In the latter case, the man's attractiveness is absolutely crucial, since he doesn't meet society's expectations, so he really has to use the "be really fucking good looking" shortcut to get around it. So for him, everything hinges on not having a shit face. Thus, I find that one's face is ultimately the most important, but I feel i's sort of reductive to not even mention all the expectations put on us by society.