(Yes I know the OP has already made his choice, I'm making this post to help out anyone else who might be on the fence about this great game series.)
1. Shadow of Chernobyl
It's the first game in the series (by release date, not by storyline), it has great mods, and being the first it has a lot of info about people in the Zone, explanations of things, and no blowouts (unless modded in).
2. Call of Pripyat
This carries on after Shadow of Chernobyl with a different protagonist, looks more polished, handles better (in my opinion), and features a new Zone map with a different take on anomalous behaviour. Great game, love it. The Pripyat Complete mod is now out, so you can pimp the visuals out even more.
3. Clear Skies
This game came out second, but the storyline occurs before Shadow of Chernobyl, and you play as a different character again. The base version of this game is buggy as hell, though I hear Clear Skies Complete (and the 1.05? patch you need to run Complete) have done an admirable job of fixing most of the problems. I never got far enough in this game (about halfway through I think, before game breaking error and updating killed my save) to know how good the story is for this game, so I would rank it LAST on the priority list (and it never goes on special, whyyyy ;_; )
Hope this post helps anyone else on the fence about which title to begin their adventures in the Zone.