From inside your LAN:
If I understood you correctly, and if you want to do this from within your LAN, simply enable screen sharing from the Mac via System Preferences » Sharing » Screen Sharing.
Then, on Windows, use any VNC Client to connect to your Mac by its IP address or host name.
From outside your LAN:
Connecting from outside the LAN is a bit more difficult. If you want to do it with VNC, you need to forward the VNC port (5900) in your router, so that all external connections to port 5900 are forwarded to your Mac Mini's IP address. However, a VNC connection by itself is not encrypted and therefore highly insecure. Thus it is not recommended to do this.
For your convenience, you can also install Team Viewer on the Mac. Use the "TeamViewer Host" version:
TeamViewer Host is running as a system service and is used for 24/7 access to remote computers, including login/logout and remote reboot - optimized for server maintenance or home-office access
This allows you to connect to your Mac from everywhere outside your LAN over a secured connection. The only thing you need to do is set up a TeamViewer account. The "TeamViewer Host" version sits on your Mac as a service and will accept connections from outside. It will start with the system, therefore "booting" into the mode you want. Once it is started, your Mac gets a TeamViewer ID.
You can also secure it to just accept connections from specific IPs and also – of course – have it ask for a password.
On your PC, you need the normal TeamViewer client to connect to your Mac by using it's TeamViewer ID.
Just give it a try.