99% of monitors retain their settings even if powered off for extended periods of time. this means they will power back on if power is cut (if they were on to begin with).
best solution, turn it on and plug it into power that is powered all the time... even when the switch is off...when signal is lost, the monitor will shut off to standby after a few seconds. When you power on the system, boop! the monitor comes back on.
no need to worry about having it not come on when it needs to.