There is a LOT to consider when adopting a BLM horse. You have to be sure that you have good, sturdy, safe fencing and shelter for a horse that is not necessarily accustomed to them. A BLM horse is not for the beginner - most of them have had very little, if any, handling. They have trust issues. They have a heightened flight instinct, and may hurt you if you don't know what you are doing. My cousin has a BLM horse. She is nearly IMPOSSIBLE to handle. He has had several horses and started many a colt, but this mare is beyond him. She finally got to where she would come and eat with him there, and he did manage to get a halter on her and can lead her some. He's had her for eight years and that's as far as he's gotten. The only thing she's really good at is trailering. Open the trailer gate and she make a beeline for it.
I have what is supposedly a mustang mare. The people I got her from said they got her in New Mexico from a friend of theirs who got a BLM mare who turned out to be pregnant. Who knows. She is a gogeous grulla color, but she's jugheaded. She's been raised around people (and abused by them - the people I got her from rescued her). She's a very friendly, spoiled pasture ornament. She's broke to ride, but hasn't been ridden in a while. When we first bought her, my daughter rode her with no problems. The owner thought she'd show how well the mare moved, but the mare "bronc'd out" and threw her. I'm working on her ground manners and will ride her again when I feel she's ready.
I guess my point is, if you are going to adopt a BLM horse, be careful and make sure you are up to the task, and/or have access to someone who is. You can't ride color, and color is much less important than temperment. Soundness, conformation and temperment are far more important that color. Mare or gelding is up to you. A gelding won't have issues with breeding drives and is generally a more reliable mount.
Whichever horse you decide on, just make sure that the two of you are a good match - and enjoy!