For tools for a mechanical setup, I use the following:
Truss Rod Ajustment:
Tross Rod Tool (usually comes with your bass, but is often just a 3/16" key)
Capo - This helps hold down the string at the first fret for convenience but isn’t essential
I have feeler gauges, but don’t tend to use them. I just eyeball it and try to get the smallest gap light can pass through.
1/64th" Precision Ruler - Most important tool for me
Saddle Hex Driver (most are 1/16" I think, but it can vary)
Understring Radius Gauges - Helps get the middle strings following the fretboard curve after you do the hight of the low and high strings.
1/64th" Precision Ruler
Intonation/Neck Bolts/Strap Bolts:
Decent screwdrivers, you don’t want to strip your screws!
Oh, and to do intonation you want a good tuner. I use the Peterson HD Strobostomp and highly recommend it.
I’ve never messed with the nut as I don’t change string sizes.
So in summary, the tools I use for the mechanical setup are:
Truss Rod Key
Capo (optional, just for convenience)
1/64" Precision Ruler
Feeler Gauges (optional, I don’t bother with them most of the time)
Understring Radius Gauges (optional, you can use a ruler)
Saddle Hex Driver
I say “mechanical setup” because there is of course polish, oils, sandpaper, etc. for body, nuts, fretboard. These are a matter of personal preference.