.0001" or .01mm
You most likely will want to keep 'the jaggies' under control during interpolated motion (ie., circular cuts and 2 axis straight angular cuts). The lower the resolution, the more that stair-step type errors show up.
Going the metric way actually gives you a wider tolerance range, but in a practical sense, you don't want to fight with a CAM system of any sort that must attempt to round numbers off to the nearest .0003 or .0004"
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)