No, I don't think gay people choose to be gay, or straight people choose to be straight. We just are who we are meant to be.
As a gay person, I don't recall ever thinking "Man, that sounds like a good idea! I'll be gay." I do remember realizing what my lack of attraction to men (I'm female) meant. I do also remember deciding I wasn't going to be ashamed of who I was, or who I loved, and that I would be the best me I could be, regardless of what the world tried to tell me.
Do we make a choice in relation to sexuality? No, I don't think we do. We do what comes naturally to us, the way in which we are wired etc. We all do what feels natural to us - straight people are attracted to the opposite sex in a sexual way, and gay people to the same sex. To force ourselves to be otherwise would be unnatural, and has been proven to be bad for one's psychological well being.