String height at the nut slots: Due to my heavy handed and semi-sloppy playing techniques, a personal preference is to have the height extremely close to just above the height of the first fret.
Fretting a string between the 2nd and 3rd frets, I'll look and feel for a string gap over the 1st fret of just less than .01 for the E, A, & D strings; and down to less than .005 for the G, B, & the high E strings. This goes along with my prefered small amount of neck relief too.