Yeah I would suggest at least a HD 6790 if you're looking to get into gaming, for some measure of future proofing.
We'll walk you through building your first system, no problem!
http://bf3blog.com/battlefield-3-system-requirements/ At least a GTX 560 or HD 6950 for decent resolutions at max settings. with 8XAA/AF, so I'm estimating at probably 1600x900. You could deal with a top 20 graphics card so long if you dialed back the settings a little; a HD 6850 will run BF3 at 1080p at mid settings >60 FPS.
http://videocardbenchmark.net/gpu.php?gpu=Radeon+HD+6850 The HD 6850 has the best price/performance as of today.
Also, I think 16 GB is rather overkill, for gaming, it would come in handy if you were looking to do video editing on a massive scale and running virtualization clusters, but for a "budget gaming PC" I honestly think 8 GB will suffice.
You should look at the equivalent Intel processors:
http://www.tomshardware.com/reviews/best-gaming-cpu-core-i3-2100-phenom-ii-x6-1075t,2859-8.html Due to their superior single-threaded performance even the i3 2100 trumps the X4 965 in games. Also, if you choose the i3 2120 you will be able to upgrade to the Ivy Bridge 3XXX processors, which support all Sandy Bridge chipsets.
I also wouldn't spend more than $50 on the PC chassis for gaming, because the cash would be more well-served being put towards beefier components.
Here is what I would choose:
Western Digital Caviar Blue WD5000AAKS 500GB 7200 RPM 16MB Cache SATA 3.0Gb/s 3.5" Internal Hard Drive -Bare Drive ($99.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16822136073 Intel Core i3-2120 Sandy Bridge 3.3GHz LGA 1155 65W Dual-Core Desktop Processor Intel HD Graphics 2000 BX80623I32120 ($124.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16819115077&Tpk=i3%202120G.SKILL Ripjaws Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1600 (PC3 12800) Desktop Memory Model F3-12800CL9D-8GBRL ($46.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231314 CORSAIR Builder Series CX600 V2 600W ATX12V v2.3 80 PLUS Certified Active PFC Power Supply ($69.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139028&Tpk=CX600 PowerColor AX6850 1GBD5-DH Radeon HD 6850 1GB 256-bit GDDR5 PCI Express 2.1 x16 HDCP Ready CrossFireX Support Video Card with Eyefinity ($139.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16814131374 GIGABYTE GA-Z77-D3H LGA 1155 Intel Z77 HDMI SATA 6Gb/s USB 3.0 ATX Intel Motherboard ($119.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128543 COOLER MASTER Elite 430 RC-430-KWN1 Black Steel / Plastic Computer Case ($46.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16811119227 Microsoft Comfort Curve Keyboard 2000 ($20.99)
http://www.newegg.com/Product/Product.aspx?Item=N82E16823109149 TOTAL COST: $669.92
Do note we haven't taken into account the price of a Windows 7 license.
Microsoft Windows 7 Professional SP1 64-bit - OEM
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116992 ($139.99)
Cheaper than the retail version, which costs $229.99
“System Builder” means an original equipment manufacturer, an
assembler, a refurbisher, or a software preinstaller that sells the Customer System(s) to a
third-party. OEM software may ONLY be distributed with a fully assembled computer system.
http://oem.microsoft.com/public/worldwide/licensing/opccomm_retail_and_coem.pdfYou are an assembler.
The parts that you quoted cost HDD($99.99)+Phenom II X4($119.99)+16GB RAM($87.99)+Sidewinder X4 KB($47.99)+500W Corsair PSU($79.99)+Asus A75 Motherboard($114.99)+HD 6750 HIS($99.99)+Apevia ATX Chassis($64.99) = $715.92. Furthermore I would like to point out that your motherboard isn't compatible with your CPU your CPU is of the AM3 socket. You'll need to get an AM3 compatible motherboard, such as the AMD 890GX series/AMD 970 series.