Marnetmar: There is no need for a 'Chocolate Quake' since WinQuake still works fine on modern versions of Windows, barring the occasional palette issue that goes away whenever the screen flashes. I have no clue on ATI, but I'm guessing it doesn't work given the number of complaints about it over on the Steam forums. I've been told GLQuake does now too, but I know in the past you had to use nVidia Inspector to point the driver settings to the correct executable, since it was looking for quake.exe instead of glquake.exe and glqwcl.exe.
Quake 2 works fine with nVidia's drivers. Nevertheless Yamagi Quake II can play it if you copy the files into the directories mentioned above. Later Quake II version, for example the one included with Quake IV and the one available through Steam, lack the soundtrack. Your Quake 2 issue sounds like your display may not be handling the resolution correctly. Yamagi Quake II will use these files instead of the CD tracks. Winquake still works fine, regardless of drivers, barring the occasional palette issue that goes away when the screen flashes. If you grabbed retail copies of the games you'd be having the same problem. Blame the drivers and lack of foresight in the coding of the GL executables themselves, not Steam.