What are some design considerations for S-Boxes?
The main consideration is to ensure no strong differential or affine properties. 

Random S-Boxes are actually not bad in this regard though not necessarily optimal. 

However Most would not trust "Random" S-boxes and prefer a Nothing-Up-My-Sleeve choice. For fear the designer may have cleverly selected the values to enable some unknown attack. We want some plausible explanation for why the specific values were chosen. 

The AES S-boxes are such, they were selected based on a simple mathematical formula, and yet can be shown to be fairly resilient to differential and linear cryptanalysis.