I just started trying to play Quake 1 on win 10, but unfortunately I'm having some graphics issues. The map appears completely black (no wall, ground, or ceiling textures) and the character models are just grey. Any suggestions on how to deal with this? (Nvidia GPU)
Try opening in Software mode (click More -> Other -> Quake (Software Mode)), are the textures black then?
What you have can be a problem with the OpenGL version of the game.
If this works, you might find software mode a bit slow, there are solutions on the forum to get it working faster: https://www.gog.com/forum/master_of_magic/game_working_super_slow
If this is still a bit slow, you can always try WinQuake.exe which is in the games GOG folder.
(WinQuake.exe is the software mode version for Windows, where as the one you get from the GOG User Interface is the one for DOS)