Re: Thanks Chris.
MS RDP is the "Windows Thing", VNC is cross platform and often on Linux by default, you have to add it to Windows.
It's usually a connection to an existing running local desktop*, unlike running X over a network, nothing is "lost" if connection is dropped, you just reconnect. So unlike X the desktop resolution is what ever it is on your target machine, the client opens a window to it, so having higher "resolution" client than remote helps.
Using a VPN to the VNC server is another idea.
[*No, I don't know how to set up a VNC server on a computer with no graphics card, though the target's keyboard, screen and mouse could be disconnected (or off), I suppose.]