The rule of thumb when turning on any audio rig is to power up the sound-creating device last — in most studios, this will be the power amp that drives the monitors or the monitors themselves, if they’re self-powered. With guitar, bass, and keyboard rigs, this will be the instrument amplifier. In live sound rigs, this will usually be the power amps that drive the mains speakers and the monitor speakers. Doing this prevents loud pops that can result from gear earlier in the chain being powered up making it to the speakers and possibly causing damage.
When powering down, turn off the amps or self-powered speakers first and wait for a second or two before powering off everything else.