NoNewTaleToTell: I'm still a newbie to the series so take this with a grain of salt, I've only played a little (maybe three hours) of S.T.A.L.K.E.R. Shadow of Chernobyl and around two hours of Call of Pripyat, and I would say they're about even.
Shadow of Chernobyl is a lot more story focused (at least in the beginning), whereas Call of Pripyat seems a bit more open (they're all zone based open world).
Though I've yet to play it myself, Clear Sky is consistently ranked as being quite a bit inferior to the aforementioned titles.
I'm not sure which has the most mods but all three have major mods available, the Complete mods. The Complete mods do some light balancing, fix a whole lot of bugs, add some new songs (original ones at that, I believe) and improve the graphics. All three are available at the mod database.
I would say stay away from the Complete mods the first time you play, they tend to break more things than they fix, CoP was uncompletable last time I tried and the balancing fixes makes the games a bit too easy if you ask me.
And you can mess around with ENB series or SweetFX by yourself, you don't need any mods for that.
You might want to try the stand alone Lost Alpha mod, for which you don't need any of the games, beware that it has a lot of bugs and deviates from the original STALKER games in terms of story and atmosphere.
As for what's the best STALKER game disregarding the mods I would say Shadow of Chernobyl.