Per the Publisher:
For the best performance you should aim to run the game on a system with at least these specifications.
Operating System: Windows® 7 64 bit
Processor: Intel® Core™ i5
Graphics: NVIDIA® Geforce® GTX 660 or higher, AMD Radeon™ HD 7950 or higher
Memory: 4GB of RAM.
Disk Space: 20GB.
Looking in the crystal ball, I don't see a $700 system in your future. My humble advice, look for a i5 4670K with a Z87 motherboard, and 8 gigs of RAM. You can grab an ATI 7950 for close to the $200 mark after rebates if you pay attention. Looking at it again, it might be possible to come close to the $700 mark depending upon what you want to upgrade. A strictly CPU/motherboard/memory/videocard upgrade reusing your other components could very well be cheaper than your budget.
.....and no, I really don't lean towards AMD CPUs for gaming builds.
I am a retired Ford tech. Next to Fords, any computer is a piece of cake. (The cake, its not a lie)
3770K @4.5, Corsair H100, GTX780, 16gig Samsung, Obsidian 700 (yes there is a 700)