The most critical material property is the elastic modulus, for elastic buckling. For thick walled cylinders, elastic-plastic buckling occurs, in which case it is the tangent modulus (draw a line tangent to the stress strain curve, the slope of the line is the tangent modulus). In the Section VIII rules, the graphs to determine B are used to determine the tangent modulus, when the stress is between the proportional limit and the 0.2% yield strength. This is the region for elastic-plastic buckling.
As stated above, the most critical geometric property is D/t ratio.