Very High is the max for Crysis3 IIRC - but even then, it's quite demanding (for the era).
A 680, I believe, was necessary at the time.
From what I can find though, a 680 these days is routinely selling for $80-$100 USD
A GTX 770 performs very similarly to a 680, is a gen newer, and sells for nearer $50 - That's what I would look to if I were you.
As for the 2600K vs anything else, what kind of prices are you considering them at?
You might be able to find a C2Q, like a Q9550 for pretty cheap, or an X5450 Xeon with a mod to work on 775 - which would be a more 'budget' entry into Crysis3.
With a bit of an overclock to a Q9950, you could see ~30FPS paired with a GTX 760 at very high.
Drop to medium/high, and you should have a pretty...