We know that the notion of handsome-ness or beauty differs from culture to culture. We can also be pretty certain that if you are regarded as handsome or beautiful in your own society you have a head start towards being favourably viewed in being selected in just about any area of life compared with those who are 'average,' and way, way above those who might be generally regarded as 'ugly.' This is the way of things, unfortunately, for the many.
If you happen to be good looking and have influential parents, ones with money, power, and prestige, and are perhaps famous in the area the 'beautiful' person wishes to enter, your future is all but assured. You'd have to do something pretty awful not to get that advantageous start.
So how important is it to have good looks in relation to success in American society? Pretty important, I'd say. But probably not as important as some of the other aspects which eventually bring success. I am thinking of determination, clarity of purpose, perseverance, doggedness, continuing education, willingness to serve, that sort of thing. Beauty might bring an initial advantage, but that is all. The real power lies in the character of the person