That cooler ain't that good, a noctua NH-D14 beats it in terms of temperatures and noise, that mobo is overpriced, the Asus P8Z77-V PRO has more features, power phases, and it's cheaper, that thermal armor doesn't help cooling the mobo, it only helps to collect dust.
For gaming an i5-3570k is what you need, no point in getting the i7, nor the 16GB, it doesn't get used in gaming, 6GB doesn't get used, 8GB is plenty.
A 670 gtx is just less ~5% in terms of performance of a 680 gtx, so getting a 670 gtx is the best value, in the future add another one, it goes a lot cheaper.
Also with that budget, it's wise to get a good ssd with at least 120/1280GB.
The keyboard it didn't found on the list, but i'm sure it goes bellow that budget with it.
My changes : http://pcpartpicker.com/uk/p/yQyf