I'll be the black sheep here and recommend Crysis as the best in the series.
I've played through all three multiple times, and the original is still what impresses me most.
This boils down to personal preference, though. I like games that give you room to breathe....some gamers find this approach boring, but it's just what I prefer.
Warhead is a fun, albeit short romp, and it's well worth getting - but I don't find it in any way superior to Crysis.
Crysis 2's biggest downfall is the utterly abhorable gutting of the FPS mechanics that made the original so impressive. No other FPS feels as good as Crysis to me - and I'm talking about a direct line to control of player movement and gunplay. The way Crytek handled integrating various positions of movement is nothing short of a masterpiece IMO, and it makes playing other FPS's feel almost robotic and fake.
Controlling the player in Crysis is like driving a precision sports car.......controlling the player in Crysis 2 is like trying to race in a Dodge Caravan. There is no lean (auto lean? I don't want "auto" player control - it sucks and just works as a handicap for players without enough skill to know otherwise). No prone. You can't pull off any of the advanced movements that the original games gave you the capability to do: flicking on power to jump up on a rooftop, and cloaking mid jump to avoid detection, then landing in a prone position to start picking people off - all accomplished smoothly as silk thanks to the ingenious interface and integration of movement and control offered in the first games.
Crysis 2? Running around like a drunk soldier and that incredibly annoying jump lag. Sloppy and dumbed-down as hell compared to Crysis. It sounds like I'm being really hard on C2, but despite how harshly I'm comparing it to the first game, it's still a GREAT, FUN game taken at face value and not compared to anything else.
So my recommendation - buy the original. If you want it to look even more incredible, there's plenty of mods that up the eye candy.
Then buy Warhead, which comes with Crysis Wars, one of the best Multi-Players out there. Maybe I'll see ya there.