As jko said, UVA is a very reputable school, public or private.
At the top schools, you'll see a good chunk of alums from the top public schools like UVA, Texas, UCLA, Cal, and Michigan. They're generally viewed pretty favorably, and on par (and sometimes even better than, depending on the individual adcom's own opinion) with private institutions like NYU, USC, and Northwestern. For example, Cal has one of the top engineering programs in the country. Similarly, UVA has one of the most reputable undergrad business programs. So it's not going to be a negative at all - and in a way is a positive because of where you went.
In other words, you'll find that if you add up the following schools, it'll account for the majority of folks that attended US colleges at the top MBA programs:
Ivy equivalent (Stanford, MIT, Caltech, Duke)
Top lib arts (7 sisters, Williams, Swarthmore, Amherst, Bowdoin, etc.)
NYU, USC, Northwestern, UVA, Texas, UCLA, Cal, Michigan
US service academies
Doesn't mean that you can't get in if you aren't from these schools, but that the folks who went to the top schools tended to have stronger job opportunities after college (i.e. getting recruited from the top banks, consulting firms, F500, etc.)
As for being gay, if it's something that is important to you (beyond just your personal life, but where you've been involved in community organizations and activism), then it's something you should definitely talk about.
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