Remotely-accessible system video card needs?

[Dooling37]

I'm going to be building out a system that will be remotely-accessible only - via SSH, VNC, or, most likely, RDP/Terminal Services. (reason being, I recently bought an LCD monitor with DVI output that is now connected to my one existing system ("system A"), and I don't want to invest in a DVI-capable KVM at this time.)
So I'll be connecting from system A - does the quality of the video card in the new "system B" matter, at all? Or will the video quality depend solely on the video capability of the connecting system A? Can RDP/VNC display at a high resolution (1900x1200)?

Thanks much for any input...