First time up, here - my question is as the title asks.
I usually start with lens correction, then white balance and temperature, possibly saturation, and then it's catch as catch can.
I'm really interested in if you go for highlights before or after whites, and shadows before or after blacks, and what is the assessment process.
Oops, I meant contrast, rather than saturation.
The recommended, preferred and most logical procedure is to follow the order in which the sliders are set within each Camera Raw tab, and start with the first tab on the left, then follow the order of the tabs.
It's by no means necessary to adjust everything, just what is needed for each shot. If you are doing all that adjusting you mention, your photography skills need a refresher course.
Read as many works by Jeff Schewe as you can.