BLM Mustangs make incredible horses and I hope that you are able to get one. Dee is right though, to adopt an untamed one is quite a large challenge and can be too much for many people. However, there are more and more mustangs that have been trained going up for sale every day plus they have the training programs prior to adoption like the one in a Colorado prison. Holding out for a horse with all the attitude and conformation that you need in the color that you want may make for a long wait but don't give up. I waited for a bay horse for about 10 years and a black one for 20 but I finally got them.
I have got 2 mustangs right now(<< one in my avatar) and someday want to get another. When I do, I want a solid black with a white star. There is nothing wrong with having a color or pattern preferance, just don't overlook other issues with the horse just because you like the color.
I don't particularly care for mares just because many of them do have their "marish" days during their cycle. I generally ride geldings. However, there are many people who like mares because they believe that they have more personality than geldings. It is all a matter of preferance. However, my brother mentioned something last night that I hadn't even thought of. He mentioned spaying a mare that would never be used for breeding just to make her temperment more level.
Good luck in your search and I hope you are able to find one.
ETA: I can't give any name suggestions until I see a horse or at least know kinda what their attitude is like. ;p