Most devices don't mind at all being powered on and off through an external switch. There may be some designs where the internal power switch also controls e.g. a soft start circuit. I haven't seen anything like that in a long time.
It is simply a myth that it is better to leave electrical devices powered on. The opposite is true: the devices will age must faster if you leave them on. And, it is a waste of energy.
It is true that incandescent light bulbs suffer when you turn them on because the cold filement has a lower resistance than the hot one, i.e. it is drawing a high current during the warm-up phase. Thus, if you want to install low voltage halogen lighting, I would recommend using an electronic transformer with build-in soft start.
Today, all CFLs have electronic transformers. They also don't mind at all being turned on of off.
There are cases where the order may matter. For example, if your audio interface produces an glitch when you turn it on and your amplifier only turns on the outputs after a few seconds to protect the speakers from its own glitch, then it would be smart to turn on both devices at the same time (rather than turning on the amplifier before the audio interface) so that the glitch form the interface would not matter.
For some cases, a master/slave power strip is a neat thing. My UPS has slave outputs. When I turn on my computer, the UPS also enables power on additional outlets that are not backed up by the battery. I use those outputs for devices that need more power, e.g. my monitors and the printer. When I am done, I turn off the UPS completely. Anything that has power is potentially a fire hazard.
Wilko