mstsc is remote desktop, essentially using a LAN connection in lieu of a kvm. to my knowledge it sucks if you’re using graphics-intensive applications. major design flaw imho.
i don’t really know kvms well, so don’t listen to me for advice on brand names
what i did this past semester is my monitor will toggle dvi / vga so i did that for video, and for keyboard, mouse, and accessories i had a usb hub that i moved back and forth with usb keyboard and mouse, etc… to make the switch quicker i had a usb cable to each computer and just changed which one was plugged into the hub.