For modern enhanced single-player, download either QuakeSpasm or Mark V, the two most useful/promising Quake source ports, and extract the Steam game files from steamapps (id0 + id1 PAKs, and the soundtrack files if you have them) into folders the source ports look for. Then start the app up and have fun. You'll be able to vastly upgrade image quality, controls, and graphics from the original this way.
Definitely look into buying Scourge of Armstrong if you want a worthwhile expansion to the original game. I recommend searching for really good custom maps and campaigns on Quaddicted, as well as mods like Quoth or Arcane Dimensions which have a lot of pro-level maps to enjoy.