SSH is the best way. Use WinSCP with Putty on the PC. Just be aware that if you use any type of KVM switch that does not do a keep alive signal on the device not in use with the KVM, you will see a lot of no device found errors.
I have a monitor with both VGA and DVI that I had the PC on one and the Pi on the other with a DVI to HDMI adapter, no sound. For the mouse It was only for the PC, the Keyboard was through a A/B switch that worked out pretty decent with the Pi not needing a GUI as a headless unit.
Ren: Now listen, Cadet. I've got a job for you. See this button? Ren: Don't touch it! It's the History Eraser button, you fool! Stimpy: So what'll happen? Ren: That's just it. We don't know. Maybe something bad, maybe something good.