Atmosphere and immersion mostly come down to personal preference and can be tweaked with various mods as well. And yes, they can be quite buggy when not patched, even more so if you mod them without much knowledge. Also of important note is that they are 32bit games and as such can bogg down on highest settings even if you have a good rig, even more so if you use resource heavy mods (this mostly goes for CS and CoP)
Yeah, as some have mentioned, start with Shadow of Chernobyl, while Clear Sky is a prequel, gameplay wise it is closer to Call of Pripyat (which is in that regard the best out of the three). So, it pretty much goes in the same succession as they were released.
As for ShoC mods or unofficial patches, personally I can vouch for the fallowing,
ZRP is a very good choice if you wish for more or less vanilla but improved experience
NEWSA+SIMBION http://stalkermod.net/viewtopic.php?f=2&t=3
Old Good Stalker Evolution or OGSE (using it currently)
For new storyline there is Priboi Story
Can't really say much about CS mods, as I have not played it as often as I have others
CoP is, as said, gameplay wise the best.
As for mods, well Misery ain't bad.
There are of course lots of miscellaneous mods out there on Mod DB and on http://www.gsc-game.com/index.php?t=community&s=forums&offset=-120 and a whole other big arse venue on the Russian speaking community side.
And as always, play vanilla versions first, then and only then start slapping on mods.
ed: While the Complete series are decent mods, personally I think there are better ones.