First of all there's something called bottlenecking which will be achieved by your CPU for its lack of ability to keep up with the strength of the GPU . So basically its when the CPU is at full usage and the GPU is idle or doing very little .
My advice is to do a full system upgrade for the 300 bucks , use whatever you can salvage from your old build like the HDD and Ram , Something that looks like this :
PCPartPicker part list:
http://pcpartpicker.com/p/XdPpQ7
Price breakdown by merchant: http://pcpartpicker.com/p/XdPpQ7/by_merchant/
CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($59.00 @ Amazon)
Motherboard: Gigabyte GA-B85M-DS3H Micro ATX LGA1150 Motherboard ($66.99 @ Amazon)
Video Card: XFX Radeon HD 7870 GHz Edition 2GB Video Card ($240.98 @ SuperBiiz)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($44.99 @ NCIX US)
Total: $411.96
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-08-26 15:40 EDT-0400
Instead of buying this GPU from the listed seller , pick it much cheaper here :
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150605&nm_mc=EMC-IGNEFL082614&cm_mmc=EMC-IGNEFL082614-_-EMC-082614-Index-_-DesktopGraphicsVideoCards-_-14150605-L010D
For 160 Bucks and the total should be around 330 Bucks with an overall better system that's very capable and will achieve these FPS , it will achieve 60 FPS if you crank down the settings to medium with no AA on 1080p.
Benchmarks :