Plug the TV in and turn it on -- Now unplug it - wait a few seconds and plug it back in --- Does the TV turn back on ?
If yes then that is all that is needed and it should work fine once you install just do not use the power button and it should always turn on when power is supplied.
If No then the TV does not remember the setting automatically (or there is a setting somewhere in the OSD for remembering the setting (ie. power on after power loss, etc.) - so will need to find the setting and turn it on or run a button to the On/off button of the TV to turn it on each time (either make the on/off switch on the TV accessible, add a hardware piece to press the button with (ie. drill a small hole in the plexi covering the TV so that you can insert something to press the button, use the remote control to power on each time, or splice an arcade button into the wiring of the switch so you can press the button to turn the TV on/off.
Or wire a button up to the tv as above and also get a smart power strip(bar) and plug the TV into the master plug ( that way when you press the button to turn the TV on/off it will also turn on/off the entire power bar )