Good topic!

Personally, I try to avoid stereotypes as much as possible and try instead to focus on the "person" behind the character. Stereotypical people are rarely very interesting in the real world, and are absolutely a bore on the written page.

I start first with an idea of what the character must do or be, and then put together a list of necessary personal traits and knowledge required for the character to accomplish his or her part in the plot. I then try to imagine the sources of those traits and knowledge (i.e., learned behavior vs. natural talents, formal/directed education vs. self education vs. personal experience). Until I know how my character needs to behave, I may have an idea about the gender, but I try not to commit to a specific gender at that point just because a role would typically be filled by a man or a woman.

For example, if my character needs to be a venerated scholar and is living in Medieval times, it is common knowledge that women were rarely (if ever) allowed to join in academic or scientific circles, so therefore the character should probably be male. But the character could also be female, which would open up entirely new avenues to explore because you would then have to explain how she was able to attain her knowledge and acquire her status given the gender-biases of the time and region. Much fun could be had with how she relates to and competes with her male peers, as well.

There are very few cases I can think of (except, of course, certain biologically-specific plot requirements, like giving birth) where the gender of the character is set in stone because of the role he or she plays.

I also try to avoid forcing stereotypical traits on my characters based on their role. For example, if you assume that a respected leader is self-confident, compassionate and intelligent, it can make things more interesting (regardless of the gender) to replace one of those three traits with something not so admirable. For instance, a leader who is self-confident and compassionate would still be respected even though he or she was as dumb as a doornail. Likewise, a leader filled with self-doubt, but is still compassionate and intelligent would also be respected -- and would also a much more interesting character.

Again, good topic! I've never really seriously thought about how I develop characters, relying more on instinct than methodology to do it. But now that I've analyzed how I prefer to do it, I have some new ideas for some old and dusty characters of mine who might benefit from a gender change.