The setup was quite simple, although not entirely out-of-the-box:
1. Bought it on Steam
2. Downloaded the Quakespasm package
3. Extracted the package in Quake's folder, overwriting some files
4. Rename the Quakespasm executable to either glquake.exe or winquake.exe. Then select the appropriate option when launching Quake from the Steam menu.
5. That's pretty much it. You won't have any music with this setup yet.
6. Remember to check that lookspring and lookstrafe are turned off and mouselook is on. Also, select a bigger resolution like 1920x1080 with 32bit colors. You're set to go.
MUSIC:
Getting the music to work will require some more work, but I won't cover it here... But youy basically gotta get the music online, either emulate a CD rom drive and mount an iso image OR rip them into the wav format and emulate it somehow.
If the music sounds funny, you gotta deemph it with sox (a commandline tool). Told ya it wouldn't be that easy if you wanted the music to work ;)
The reason for that is that the original quake used the audio CD format. It didn't have actual music files like modern games do.
WHY NOT JUST USE THE BUNDLED GLQUAKE?
I had troubles myself trying to play with that. The resolution can't be changed from within the menus and although I found tutorials on how to change it from Steam's launch options, the game just kept crashing... Just do yourself a favor and download a new engine like Quakespasm. The process will be less painful and hassle-free.