To me, a classy man is respectful and sees a woman as a person, not a place simply to deposit his penis. He recognizes that she has a personality, talents, an intellect, etc. and seeks to get to know HER, not just her vagina. He's not going to lead with the sexual foot if he's seriously interested in making a good impression.
I don't search women's profiles online, but I've been told by enough guys that there are plenty of women online who, by their profile or pix, make it plain that they are seeking something casual. So why bother with someone who makes it plain that she is not?! (Yeah, I know: the challenge. Challenge, schmallenge.)
As for being straight up and to the point, if that's the route he chooses to take and he tells me up front what he is seeking - in a respectful way - and I tell him I'm not on the same page, then he needs to say "Thanks for your time" and leave me alone instead of trying to cajole me into seeing things his way. I'm ok with that. That's being classy as well.