I don't think I would be comfortable describing transgenderism into one simple description.
I would make the hypothesis that being transgender is in fact more of a choice than those who identify as transgender would lead others, and even themselves to believe.
I am also more comfortable stating that the main reason those that are transgender would be upset at that idea of choice is that it is used extremely pejoratively in popular use, which tries to have an effect of delegitimizing the individual. Religion was brought up earlier. One "chooses," in most cases, especially in western culture, to be religious, anti-religious, and everything in between, and that is accepted as being a defining characteristic of that person. The same courtesy generally isn't provided to transgenderism.
I guess to wrap back around to the original question, I think in individual cases, the answer to one or all three of your items could be yes. I do not and would not even begin to guess the percentages to the questions. If I could repurpose the question, "Are people transgender because of biological, neurological, or cultural reasons?" I would answer, "Yes. All three."
That's why there's no easy answer and why even with a spectrum, homosexuality (or any other unusual sexual attraction), as a cultural device, is so much easier to define and analyze.