Let me offer my perspective as a fairly successful but very much an average-looking guy.
I'm ethnically East Indian, short, and wear glasses. I am divorced and my wife has custody of our kid. However, I consider myself quite successful (formerly investment banking, have had a few startups and a hedge fund, now management consultant doing private equity, making almost half a mil a year), well-educated (3 degrees, including one from Harvard), athletic (do a lot of rock and ice climbing), interesting (traveled a ton, play the violin, ride motorcycles), multilingual, well-read, and if I may say so, reasonably smart (at least looking at my test scores). I dress quite well (thanks to my job, I have invested in some great bespoke clothing) and being a short, geeky kid, I have had to work on having a good personality. And being a brown man in America, I have had to learn to look sharp and professional, in case a cop or a TSA agent thinks I am up to no good.
My primary filter for women is reasonably good looks that I am attracted to, followed by their education and socioeconomic status. And how smart and engaging they are, because that would affect how my family, friends, and coworkers would perceive them. The last part is an undeclared but often subconscious component, because if my girlfriend looks like an idiot in front of my friends, then it makes me look bad. She can be the hottest thing ever, but if she comes across as a vapid narcissist, then it would be a deal-breaker.
Many great looking girls tend to be somewhat superficial, so I would have a hard time having a relationship outside of the bedroom. Not all, though - some of the truly gorgeous girls tend to be more humble and awesome, which is ironic. A girl who's a 6 or a 7 thinks she deserves the best men, whereas a girl who's a 9 or a 10 tends to be much more open. Why? I really do not know.
So, I genuinely look for women who are smart, interesting, and are compatible with my worldview. What does this mean? Well, I enjoy traveling and adventure. I love reading a lot and music. I am quite liberal and hold strong opinions on things like religion, animal rights etc. The outdoors are a huge part of who I am and I find that women who are well-educated and aligned to my values are usually naturally compatible on many of the other topics. You cannot be well-traveled and remain a bigot. You cannot read a lot and remain small-minded. You cannot love exploring the world and not want to help it.
Women usually filter me on one of 3 criteria - short, brown, has a kid. The ones that look past these three criteria tend to be more open minded. So, it becomes a self-selecting mechanism. The ones who reject me instantly never find out how much I am worth or what I do for fun.
I have found American women in America to be much more picky than women from other countries. I have lived and worked in Germany, Spain, Portugal, Argentina, Denmark, and Sweden, and most recently I moved to Australia. In all 3 countries, I have not had any trouble dating extremely attractive and successful women. In contrast, I have lived in Ohio, and I must say that it was almost impossible to date any successful, good-looking woman who was not obese.
Ironically, my current girlfriend is an American I met here in Australia. She is half Danish, incredibly tall and beautiful, and is pursuing her PhD while running her own business. She has lived in and traveled to way more countries than I have, and has a worldview that is quite amazing. Remember the part I mentioned about a 9 or a 10 being humble? That's her - to her, looks are irrelevant, and she genuinely wants to be with someone she finds smart and interesting.
I was intimidated by her every step of the way. She hit on me first, she kissed me first, and she made the first move for sex. The thing is, successful guys who are lacking in other areas (height, ethnicity) are often made to feel inadequate, and some women look past them. We want to be with women who are willing to genuinely care for us. I know my girlfriend doesn't care about my career or my net worth, because what's important to her is the kind of person I am.