The nut height is out of the equation as soon as you fret a note though. I know relief and string height are personal preference, but I always go for the below as standard on my basses:
Relief - fretting the first fret and last fret (with my elbow!) on the E string, I should be able to slide a .50mm pick under the gap above the 8th fret without any gap or raising the string
String height - Using a steel rule, I fret the first fret then measure the gap between the 12th fret and the string, then go in increments as below:
E = 4/32"
A = 3.5/32"
D = 3.5/32"
G = 3/32"
This might be a bit higher than standard but it's not too high and works for me.
Once I've set up as above, I usually have little to no fret buzz. If I do, on fretted notes, it's highly likely to be a high fret issue further up the neck. I've also experienced the dreaded ski jump! Also, on open strings with this set up, I've found that any buzzing on lower frets is usually a nut height issue.