The newer games are tuned for hardware that hasn't come out yet so let's get down to business.

How about Tomshardware's Red Devil? You can drop the SSD and something else to meet your price point.
How about what you have and maxing out the RAM and popping in a video card from this list?

I'm sure you've read the following.
"Our tests demonstrate fairly little difference between a $225 LGA 1155 Core i5-2500K and a $1000 LGA 2011 Core i7-3960X, even when three-way graphics card configurations are involved. It turns out that memory bandwidth and PCIe throughput don't hold back the performance of existing Sandy Bridge-based machines. ",3106-4.html

Your existing machine might be closer than you thought.