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Some may think I'm splitting hairs. ...but meter first then focus.
I'd say it depends: if the subject is moving but under steady light than metering first makes sense; but if it's a stationary subject under changing light then focusing first makes more sense.
Typically, I mix metering and focusing, but with a prediliction for metering first, even when lighting conditions vary. But I don't shoot so much action or bird-in-flight as others.
I typically shoot in Manual & Raw & back-button-focus. I will meter a scene, taking note of readings at several directions if there is shade or other static variation in lighting depending on direction. Then I confirm those with the HistoBlinkyMeter and may adjust them upwards or downwards according to EttR principles (Expose to the Right).
Then while I'm shooting, I focus as needed. If the action or the view moves into an area with different lighting, I adjust the exposure on the fly according to my previous metering and the current reading (with mental notes about compensation due to EttR) and continue shooting.
If the metering changes due to clouds moving in or out (instead of shifts into differing static lighting), then I remeter including checking the HistoBlinkyMeter and applying EttR. If the clouds revert back to the original lighting, then I've already got that on board.
This is not done by using Tibetan memory tricks, but rather by having a base idea of the exposure needed and also of what compensation to apply as needed for different lighting. But I do chimp the LCD and consult the HistoBlinkyMeter on various previous shots as I am able.
I learned this kind of approach from match needle metering for film. I'm not fussy about needing +/- 1/3 or 2/3 stop adjustments in Raw conversion or B&W negative printing, and I don't try to lean on the EttR too much if I am shooting loosely. Of course I will take the time for careful metering if I am shooting something very deliberate like a quality landscape, architecture, or portrait session. (I no longer shoot colour film).