worst system is ft-in, an architectural/contractor's favorite that is tedious, but does have some use for looking at larger dimensions. in my shop, we use inches-decimal inches, which has all the advantages of metric (no fractions), works with US raw materials, which are typically measured in decimal inches, (or major fractions, usually to the 1/16th, which i can deal with). all my cnc machines, cad drawings, digital calipers, tiger stop, are in inch-decimal inch. biggest problem is scales and tape measures. starret makes rules with 1/32-1/64th on one side, 1/50, 1/100 (basically decimal) on the other, but i can't find tape measures like that and my martin saw has 64th's on the stops!#%#@%.
our shop's common smallest measure is the "'thou" .001" (we are machinists), and we are comfortable expressing tolerances in 'thou, as in: good to five 'thou, or if really being tight, to "tenths" or .0001"
when we scale cad drawings, i prefer 1:5 or 1:10, but that drives architect's crazy, because they need a special fractional scaled ruler which ain't decimal by a long shot.
speaking to the many wacky imperial measures:
look at ferrous vs cupric sheet metal gauges (aluminum sheet is measured in decimal inches), number drill gauge sizes, pipe dimensions (distinguished from "tube" dimensions, threads per inch (40, 32, 18, 13, 8, etc.)
or buy and older british motorcycle and play with whitworth bolts and threads