Powering up everything at the same time was taught to be inadvisable. Mostly because the monitor could cause dips and spikes in the line voltage for a fraction of a second and this could possibly mess up your digital circuits connected to the same line (like your computer).
The rule I saw in many manuals and was taught in school was to generally turn on the biggest power-suckers first:
1) Monitor
2) Speakers
2.5) Extertnal disk drive if applicable
3) Computer
Generally it was always more or less assuemd you'd turn on the computer last.
Ideally you turn them off in reverse order. I suspect that the power-off sequence isn't so critical as the power-up sequence.
I, and the other people I know who follow these rules haven't had a computer or hardware failure in 25 years. The people who power things up all together via powerbar, or do it in the wrong order are the ones we always notice with continual problems.
It's worth adopting, no harm can come from it and you'll probably extend the life of your equipment.
