First thing to adjust to lower action?

[moosie]

I always start with the old strings that are on the guitar assuming they are the gauge that I will end up with.

Ah yes, assuming that.

 

[Tweeker]

Fender published this Telecaster Setup Guide a few years back. I saved and reformatted it so I could reference it.

Some good stuff here.
Still, a bit of a chuckle reading this: “No matter what gauge of strings you use, for the best tuning stability we recommend using Fender strings”

 

[Karlx]

I like low action and skinny strings and equal string height. I'm able to get 3/64" with 9 to 42. Higher than this it becomes too high effort to play difficult lines. I really wish PLEK wasn't 1/4 the price of a decent guitar. But I can really gauge the relative levelness of the frets on a new guitar simply based on how easy it is to achieve my setup out of the box.

Shimming increases bridge break angle which stiffens the playing string, which can reduce buzzing at a given string gauge and string height. If using locking tuners, I actually want to wrap the low E and A to get a sharper break angle behind the nut for the same reason. I wish locking tuner makers would reduce the post height across the board, not just on the trebles. With zero wraps, my Fender set has the E and A too straight behind the nut, so I have to wrap on just those two. And it is precisely the lack of wrapping, and nothing else, that makes locking tuners more tuning-stable.