I recently completed the "Know Your Breasts" bra-fitting guide at herroom.com, and it gave me a lot information on how to fit my individual shape. It is found on their website beneath the big orange banner to the right of where it says "brafitguide". It is abbreviated as "KYB Bra Finder." Although it was designed for women, completing it for various scenarios might give you some additional insight into recommendations on how to fit some of our differences.
I don't have enough experience with bras to have a determined a favorite material, although like I said earlier, it shouldn't make me sweat or call attention to itself under a shirt. As far as concealment goes, I'm interested in concealing the fact that I wear a bra, but I'm past the point of being so concerned with concealing the fact that I have breasts. They're there and they're pretty obvious if anyone looks closely enough. Also, I've reached a point in my life (64 YOA) where I'm less concerned about what other people think and more concerned about what is comfortable and good for me. I care more about taking care of my breasts now that they're here.