Hey, I know you wanted under $1000, here's $1020, less after rebates. I'd recommend catching a similar monitor on sale for slightly cheaper if you're stuck to $1000. Also, speakers look a tad extraneous, but it's you not me. This Intel build will perform much better for gaming. The DDR4 memory will give a little bit of performance, and will become the standard in the future. If you're looking to cut a bit, you could go for the 6400, but again, I think there's other places you can cut that would not affect the performance of the computer. I'll format this post nicely if you give me a few minutes.
http://pcpartpicker.com/list/frpzYr