As other have mentioned, you'll want to enable "Power on Boot" in the bios. You might also enable "Wake on LAN" as well, that way you can wake up the miniPC without needing to power cycle.
You'll probably need to enable automatic sign-in on windows. I know that the Windows Remote Desktop will load with windows, but i suspect some 3rd party programs might only load on user login, meaning that if, for whatever reason, you're booted to the login screen, you might be in a bit of a pickle.
If your miniPC has Windows Pro installed is there a reason to use TightVNC instead of the Windows RDP?
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