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CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Newegg)
Motherboard: MSI 970A-G43 ATX AM3+ Motherboard ($69.98 @ SuperBiiz)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($52.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.98 @ OutletPC)
Video Card: XFX Radeon HD 7850 1GB Video Card ($129.99 @ Newegg)
Case: NZXT Phantom (Black/Green) ATX Full Tower Case ($95.99 @ Amazon)
Power Supply: PC Power & Cooling Silencer MK III 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($79.99 @ Microcenter)
Total: $598.91
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-16 23:36 EST-0500)
So I just took your budget and did an overhaul. Here is what I came up with for the parts you listed.
The CPU is a good budget CPU that will be able to handle medium-high graphics cards.
The memory will work well in the motherboard's dual channel.
The case has USB 3.0 headers and is a full tower to give you maximum airflow amongst all your components. Remember, the number one rule in gaming is COOLING. If your parts fry, you're dead in the water.
The HDD will be enough to last you a long time. You can eventually add an SSD for your OS.
The power supply is very reliable and can handle medium-high graphics cards.
The GPU will be able to run most games on medium to high (and older games such as the Fallouts or Skyrim on Ultra).
Couple concerns, you didn't list your need for Windows so I assumed you already had it. Be aware though that Windows will be another ~$85. Also, you didn't list an optical drive. A DVD drive runs around $15 so you should be okay there, but just wanted you to know.