Trying to buy a new computer..

[Fiorana]

If you're looking for the cheapest PC that can easily handle this game, I'd take a good look at this build. It's $100 cheaper than the ones you listed in the OP and will perform better too.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($116.58 @ Microcenter)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($54.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($49.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.99 @ Newegg)
Video Card: MSI Radeon HD 7850 2GB Video Card ($119.99 @ Newegg)
Case: Thermaltake Commander MS/I Snow Edition (White/Black) ATX Mid Tower Case ($49.99 @ Mwave)
Power Supply: Corsair Builder 600W 80+ Bronze Certified ATX Power Supply ($29.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.00 @ Amazon)
Total: $565.52
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-02 05:52 EST-0500)

If you still have some room left in your budget, upgrade the GPU to a GTX 660, GTX 760, or Radeon R9 270X

I approve of this build, although I would get an aftermarket cpu cooler though.

[Zheri]

I approve of this build, although I would get an aftermarket cpu cooler though.

It's never a bad idea to get one, but it isn't really mandatory if you aren't overclocking. Given the OP's experience level I assumed this would not be the case. Also, I wouldn't recommend it anyway. It will increase the operating temperature and decrease the life of the CPU for little to no gaming performance gain. Overclocking this GPU, however, is certainly something you want to do. The MSI Afterburner program that comes with it is as easy as moving a couple sliders and the card itself is a beast in this respect. I have the same one in my PC and I run a ~35% OC on it and still never see temps above 60°C.

Also, forgot to mention last night, I do live in the Philly area (Downingtown to be specific), so if you are completely stuck and not too far away I could lend a hand.