Options for coaxial to ethernet

I have recently moved into a house with a coaxial cable installed from the ground floor next to the router, through the ceiling to the upstairs bedroom. I have a desktop PC with no WiFi upstairs and I would prefer to have a wired connection then to buy a WiFi adapter. Is it possible to hook up the coaxial to the router (Sky) and then to my PC, both of which only take ethernet connections? Where the cable reappears upstairs is in a different room to my PC so I'll need to run an ethernet cable from that to the other room.

Are coaxial cables actually faster than WiFi or would I be better off just getting a WiFi adapter?