Fret the second fret on any string, the string should just about 'kiss' the first fret. If it's laying on the fret, shim it at the nut, if there's any measurable distance, lower it. Having the nut set right will only affect buzz on open notes. As soon as you fret, the nut could be non existent, it's irrelevant.
For the action on the first to 10th frets, this is what the truss rod does. Fret the 2nd and 10th fret and look at the 5th. Again, the string should just kiss. If its laying over the fret, loosen the truss rod, which adds curvature and relief, if it's any measurable distance over the fret, tighten - straighten and lower the action.
From 10-12th (depends on guitar) upwards, this is adjusted by the height of the bridge. You should aim for about 1.5-2mm relief over the 24th fret of the high E and no more than half a mm difference on the lower strings - which should be higher. Or 0.75-1mm over the 12 fret.