Like people said, it depends. But even you shave or not, be clean. I shave every morning for work and every night before we go to bed because my wife likes that way. There is a saying like: "If a man shaves in the morning, he loves his work; if a man shaves at evening, he loves his wife" or something like that, you got the idea..
LOL. Funny way to word it. I think you are right actually. It is nature to have facial hair. Just go with it. But keep it neat. Like I said before, I think it really depends on the woman, but don't let what women think effect how you dress/act/look. Just do your own thing and be yourself and start hitting on women. If she doesn't seem to be interested or is wasting your time then quickly/politely move on to the next. Different strokes are for different folks so if girl A B and C don't like you then girls D and E might, and certainly girls J or Q or Z will. So fuck what they think and do what you want.
It depends on the girl and the guy. Some guys suit beards or the "rough" look more than others. Then there's some guys who tried to grow a beard and just can't, which looks terrible. I normally have the "Rough look"and most girls prefer that to clean shaven, on me at least.
clean is better where majority of girls like it. Unless you are an artist who need to be stylish always then you can keep beard.