i'm kind of biased towards Quake 2, myself, playing it all the time when i was younger. i still have fond memories of it and find the single player campaign to be actually really fun to play, despite the engine feeling a bit 'wobbly'.
Quake 3 Arena i got some time after. i was rather surprised that it was supposed to be a multiplayer-oriented game and never thought that high of it. i found it a bit hard as a result when i was little. maybe i should fire up the game again though, even though i'd prolly have no one to play the game with, lol.
Quake 1 is something i didn't play until several years later, and that was without music. despite that, though, the no-music thing actually works pretty well for the game's grim atmosphere! i hope i can get my hands on a proper disc of the game, though, since when i looked up a video with the soundtrack enabled, it was beyond magical and immersive. realistically, Quake 1 is probably the best game in the franchise thus far. the single-player is really fun to play, the controls are fluid as fuck and the art-style makes the whole place seems so grim and dark. is suspect MP is also very good, as well, and has been one of the stronger aspects of the game.
i've only played a bit of Quake 4. i recall that it was rather boring and restrictive, moreso than Doom 3 was. why all the bloody marines everywhere? would be more fun if it was only you against them. not so realistic? meh, who cares, it would have made the game a lot more fun, i think.
so, to sum it up: Quake 2 has best SP from a nostalgic point of view, but Quake 1 probably has the best SP from a more objective perspective. Quake 3 might be a really fun MP romp, but i'm not much of a multiplayer person, so i might never know. Quake 1 might have really good MP, as well. Quake 4 was kind of boring and unsatisfying, to me.