I'm pretty sure Battlefield 4 uses as many cores as you can throw at it (or modules, whatever they are calling them now a days) so a strong case could be built for AMD on this front. For about $200 you get the 8350, which isn't a slouch by any means. Used to be it was about as good as a i5, assuming you overclocked the AMD a touch.
So you can get a decent 990FX motherboard (brand and model depend on your preferences and availability), and that'll give you sata III compatibility, SLI and CFX out of the box ready, and be ready for when Steamroller hits (That, from what I remember, is going to be AM3+ compatible. Could have changed, but AMD is usually very good about making a socket last a few generations.)
Now I haven't looked at benchmarks and if the game Battlefield 4 is a Nvidia favoring game or a AMD favoring game. As a personal rule, I like Nvidia over AMD, but go with what works for your situation. Check out some reviews and see what they say. As for money, always go mid-range. Especially if your kind of on tight constraints financially.
So with a GPU, CPU, and MB let's assume that's about $600-ish spent. Now you gotta make a decision. I would say spend a hundred bucks on a 128 GB SSD (I like SanDisk, cheap and fast, and they produce their own products. It's not some re-branded item.) So now your at $700.
You need an OS, so I guess Windows 7 Pro would be best. Kiss another $130 good bye.
Your sitting at $830, and still need RAM. Go with 8 GB of 1866. That's normally about $80. Your now at $910, not including tax.
Use stock cooling if you can tolerate it. If not, get a Cooler Master Hyper 212 EVO. Those are about $40. Your now up to $950.
I didn't mention a power supply, but I think you can get a nice Corsair TX650 for $80. Now you're over budget but you'll have quality parts. A minimum of $ 1030, not including tax or what a case will cost you.
I like the Antec 300 personally. Cheap (~$50) and effective. Not so great for cable management, but if your not afraid to spend the time routing cables, you can make it look half way decent.
Now you'll be at $1080, not including tax. Throw another $20 for a simple DVD-RW drive.
So, about $1100, and a decent rig. Best of luck!
PCPartPicker part list:
http://ca.pcpartpicker.com/p/1D6to
Price breakdown by merchant: http://ca.pcpartpicker.com/p/1D6to/by_merchant/
Benchmarks: http://ca.pcpartpicker.com/p/1D6to/benchmarks/
CPU: AMD FX-8350 4.0GHz 8-Core Processor ($199.99 @ NCIX)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.99 @ NCIX)
Motherboard: ASRock 990FX Extreme4 ATX AM3+ Motherboard ($153.80 @ Newegg Canada)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-1866 Memory ($68.30 @ DirectCanada)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($66.98 @ Newegg Canada)
Video Card: Asus GeForce GTX 760 2GB Video Card ($249.00 @ Canada Computers)
Case: Antec Three Hundred Two ATX Mid Tower Case ($49.99 @ NCIX)
Power Supply: Corsair Enthusiast 650W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($74.88 @ Canada Computers)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($19.99 @ Canada Computers)
Operating System: Microsoft Windows 8 (OEM) (64-bit) ($97.99 @ NCIX)
Monitor: Asus VS238H-P 23.0" Monitor ($139.99 @ Memory Express)
Total: $1150.90
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-12 22:02 EDT-0400)
This is what I came up with, could you find some places for me to knock the price down.