Does it matter which component I power up first?

The reason you turn on the amps last is to avoid amplifying any turn on transients from source or upstream components. Yes, some of them emit some pretty intense transients, including my Nagra PLL

Lupinthe3rd, when you get as old as some of us sometimes you tend to forget things. :^) You are correct, of course, that your method works fine as well.

As many of those who responded above have said, proper practice is to turn the amp on last and off first. And I would add that after turning it off, it would be a good idea to wait some seconds before turning off the upstream component(s), until the amp is no longer capable of producing sound from stored energy. IME some solid state amps can produce an output for most of a minute after being turned off.

Whether or not failure to adhere to that sequence will cause a problem is obviously dependent on the design of the specific components. In many or most cases it won't result in a problem. But there is no point to taking any chances.

Also, in a situation where a separate preamp and power amp are being used it is entirely conceivable that circuitry in the preamp that is located "after" (i.e., downstream of) the volume control could generate a turn-on or turn-off transient. Having the volume control turned down would not help in those situations.

Many years ago, as a result of a momentary mental lapse I either plugged or unplugged (I forget which) the AC power to a Mark Levinson ML-1 preamplifier (which does not have a power switch, as it is designed to be left on all the time), while its output was connected into a powered up 200 watt amplifier. The result was torn surrounds in the woofers of both speakers.

Regards,
-- Al