For console releases, Quake 1 & 2 had great ports on the N64. If you can't stand the N64 controller (like myself), then there's a port of Quake 1 on Saturn, and Quake II on PS1. Obviously the graphics aren't as good on those ports, though.
Quake III: Arena was released on Dreamcast, which I enjoyed. But there were also later ports and versions on PS2, so I'm not sure which is better. And I know nothing on Quake 4 other than the fact it's on XBox 360, I don't know how good it is.
As for Unreal Tournament, there's a very fun version on Dreamcast. But they released Unreal Championship for later consoles, too. So you probably want to go for that (but I haven't played Championship, personally).