There is no difference in performance between coax or twisted pair in this application.
There are only two real performance improvement you could make. Connect your LAN computers into a gigabit switch (or router). This would speed file transfers between wired computers in your home. You could also use your own wifi node/router. This could improve your wifi speed ... or not.
If you've got 802.11n equiped computers attached via wifi, getting n equiped wifi would be your biggest bang for the buck.