Help with budget gaming build

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($112.99 @ NCIX US)
Motherboard: ASRock 970 Pro3 R2.0 ATX AM3+ Motherboard ($59.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1866 Memory ($75.60 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.98 @ OutletPC)
Video Card: MSI Radeon R9 270X 2GB Video Card ($164.99 @ Newegg)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($19.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $604.51
Prices include shipping, taxes, and discounts when available

this is the best you can do with new parts, and it will not be that much faster than an xbox one.
 
PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 750K 3.4GHz Quad-Core Processor ($79.49 @ OutletPC)
Motherboard: ASRock FM2A75M Pro4+ Micro ATX FM2+ Motherboard ($59.49 @ Newegg)
Memory: Kingston Fury Red Series 8GB (2 x 4GB) DDR3-1866 Memory ($72.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: EVGA GeForce GTX 760 2GB Superclocked ACX Video Card ($229.99 @ Amazon)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($19.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $627.91
Prices include shipping, taxes, and discounts when available
 
Solution
Use PCPartpicker.com to pick out your parts, it has a compatibility filter, from there you can fine tune with sales and items not listed by pcpartpicker. You have an 1150 socket processor and an 1155 motherboard. How about something like this, faster video card, top tier PSU, Win 8.1 x64 Not sure what other parts you need or not, but this is a whole computer without keyboard and mouse.

http://pcpartpicker.com/p/bynvqs
 
Ok i change my build for one reason.

I add you the same CPU from intel the G3258 because its hanswell and you can add it in an H97 motherboard.
I did that because you can add in this motherboard in the future an 5th generation CPU from intel, Like I7-5770k*
Take a look.
You can also buy a aftermarket CPU Cooler in the future like Coolermaster Hyper 240 Evo and overclock your CPU for better perfomance.

I think you can keep it 1-2years like this and in 2 years you can buy an I5-5670k* and a new GPU like GTX900series.
You can add more ram if you want, better PSU if you want, anything you want in the future and take the max perfomance.


PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($74.99 @ Amazon)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard ($76.66 @ Newegg)
Memory: Kingston Fury Black Series 8GB (2 x 4GB) DDR3-1600 Memory ($69.99 @ Amazon)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($49.99 @ Amazon)
Video Card: EVGA GeForce GTX 760 2GB Superclocked ACX Video Card ($229.99 @ Amazon)
Case: NZXT Gamma Classic (Black) ATX Mid Tower Case ($19.99 @ Newegg)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($25.99 @ Newegg)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $637.58
Prices include shipping, taxes, and discounts when available