isn't the Chicago school pretty much a variety of the Austrian?
What? No, not at all, even though they often come to some of the same conclusions in support of minimal government interference.
I thought Hayek was instrumental in developing the Chicago school and the thought of people such as Milton Friedman?
While Hayek represented the moderate wing of the Austrian school, he still was unacceptable to the Chicago school. There's a reason why, when Hayek was invited to teach at the University of Chicago, it was with the Committee on Social Thought, not with the Chicago school of economics. There was a book I read a few years back called
Vienna & Chicago which does a decent comparison of the two schools. The Austrian school is the true free market school, while Chicago is far less consistent and principled.
Anyway, though I have my disagreements, the Austrian school certainly makes the most sense among those listed here. Economics is not a science in the way that physics or chemistry are; it should not be treated as if it were.