If I were you I would wonder if you really need such a powerful system. If you are close to your budget (As the title suggest you might be) you could cut down on some of the parts you mentioned and still get fantastic performance. For example, if you are just going to be doing a lot of gaming you likely won't need 16GB of ram, so you could half that to 8GB (2x4GB).
If you are interested in cutting down your budget, I would suggest stepping down to an Intel i5 processor. I hear the quad core i5-3570K has great performance, and you shouldn't notice a difference between that i5 and the i7, as they are both quad cores with similar speeds. I personally have an i5-2500K and I haven't yet met a game it can't handle.
Keep in mind that if you do decide to switch to the i5-3570K you will need to pick a different motherboard. The i7 you picked is socket LGA2011, while the i5 is socket LGA1155.
In summary, the GTX 670 is a beast and should handle those games with ease. 16GB of ram may not be needed, 8GB may be more appropriate if money is a concern. The i7 is very powerful, but if you are close to your budget you could save money on an socket LGA1155 i5 and still have fantastic performance.
Edit: I see DJDeCiBel beat me to the i5-3570k recommendation