About to do my first setup

Without resorting to luthier/guitar tech specific tools; normal tools for measuring a bass/guitar's action could consist of feeler gauges, 6" mechanic's rule in 64ths and millimeters, fractional drill bit shanks. Nickels, dimes, quarters, and credit cards can also work. The calipers you speak of whether they be digital, dial, or vernier will only work in measuring the nickels and dimes after the fact. They're not really useable for direct measurement on the fretboard.

I use a capo for holding strings in place. For removing the neck on my precision I place the capo between the first and second fret.
As an aside, I also use the capo as a third set of hands when replacing strings after I've drawn them all the way through the bridge and up past the tuners. It holds them taught, ball end nice and snug in the bridge/trapeze while I'm fiddling with the cutters/end of strings and tuners.
In fact, it's the only thing I use it for and was bought specifically for changing the strings on my guitars.

I keep my fretboards clean by wiping with a damp rag and drying almost immediately. I leave them damp just long enough for the water to act as a mild solvent. All crud is easily removed this way. I've cleaned really filthy fretboards by scraping from fret to fret with a sharp item. A credit card, or sharpish piece of plastic work well for this. I've even used double edged safety razors (the kind most of us used 50 years ago) as they are nice and flexible and fit any fretboard radius.

Have fun.