VNC variants can be set up on custom ports and with encrypted connections
UltraVNC is my preferred variant, but it matters little. I find bit slow, and patience testing at times.
RDP connections is I prefer to use often.
When set up you can easily RDP from another computer in the same LAN, from the My computer >> Network list. Just right click and select 'connect with remote desktop connection'
I have been known to TV to a machine in a network and then RDP to another, or even RDP to the server, then (sub) RDP to the remaining workstations. RDP is great if you want to print stuff, but lousy for sharing microphone or video (sound from the rdp works well)
Both of these above work with unattended computers
There is some other suggestions from the main page of this forum (scroll to the bottom of the page) although not many offer Unattended Access
HTH
btw, not my forum. I just hang out here occasionally...