THE 840 PRO is faster but the 830 is almost as fast for less. I don't think you'll notice the speed difference at all.
The corsair HX750 gold is pretty solid and a great alternative option to the AX, i don't think I've ever heard anything bad about it. Just don't buy the HX650.
Find a reliable MB with only features you need instead of the super deluxe everything edition. More features, more heat, more failures, more money. I hear good things about the Asrock z77 extreme4/6 and it's cheaper in most circumstances. I think Asus makes Asrocks anyways. Unless you want to do extreme OC, there's no point in paying $200+ for a MB.
If you want the K editions of the i5 and i7 ivy bridge, you will lose some power savings features. I suggest you look it up first before you you decide to go with K editions. I have the 3570k and i haven't felt the need to OC it for anything yet. I run everything on a 1080p 27" monitor. Vsync @ 60hz every game with no problems.
As for the 670, it's a good choice but if I'm running 1080p and not really going to change it for a while then I'm not going to bother going that high. A 660ti will run just about anything on max @1080p with playable fps. With the next generations from AMD and NVIDIA just around the corner, you might want to think about this before you plunge.
16GB is a good start. I normally would rather G Skill memory as they are generally cheaper and perform just as good as the other brands. Read the reviews on newegg to see which one is best for you.
I have no suggestions for the case if you don't at least give me a clue to the size you want.