You've got some great stuff here! Top MBA programs will like your military leadership experience and GPA, and the first-generation component is always an added value as well. I generally ignore the URM component in assessing chances, because it is hard to assess quantifiably.

Does all this differentiation mean that you can squeak by with a lesser GMAT? Not necessarily, IMO. What it means is that you are coming in strong, and a competitive GMAT will have even more added value. I always say, look at the median GMAT of accepted students at each program, and figure that's your minimum. Some people get by with less, but don't think in terms of being one of those exceptions we've all read about; think in terms of making the GMAT a neutral-plus so that the admissions readers can focus on your story.

So to be specific, I'm thinking 730 would make the GMAT a non-issue, and higher than that would make it an asset. I might differ from other advisers in that I don't think you'd gain much competitive advantage in going beyond 730, because you have so many other strong areas to highlight and possibly develop further in advance of your application. In any case, I am guessing that with your academic background, 730 will be totally doable for you.

Good luck!
Margaret Strother