I've come to the conclusion that sock "putting away" is a complete waste of time and energy. Pile of clean socks, thrown in a drawer. Takes 5 seconds to find.
I ball/connect my low cut socks. Boot socks are connected at the top. I also have my boot socks in one drawer (cotton and wool) while my dress, athletic, and hiking socks go into a different drawer.
Since work went casual I only wear dress socks a couple times a year. I just have 30 pairs of the same exact socks so they are just laying in the drawer in a row. Take the socks from the right, put the clean ones on the left.