that will get you the HDMI over a distance using CAT6
Then you would use something like:
The second is only usb 1.1, but for a mouse and keyboard you probably don't need much more than that. You would need to wire each end directly to each side using CAT6 and there might be other devices to run USB 2.0/3.0 over CAT, but these work fine for me. I run them about 85' between my kids' room and the living room so they can watch netflix and play minecraft.