Good gaming build for under $800, how good will it play?

Would like to play Borderlands 1 and 2, Sims 3, Kingdoms of Amalur, Command and Conquer 3, Simcity 2013, Minecraft, a little bit of Crysis 1& 2, Saint's Row 3 and 4. Would like to play on "High" or higher if possible at 1080p and around 40fps (I can't really tell much beyond probably 50 fps at the most, anything higher become bragging rights.)

PCPartPicker part list: http://pcpartpicker.com/p/2OvBR
Price breakdown by merchant: http://pcpartpicker.com/p/2OvBR/by_merchant/
Benchmarks: http://pcpartpicker.com/p/2OvBR/benchmarks/

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($33.24 @ Amazon)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard ($134.99 @ Amazon)
Memory: Kingston HyperX Blu 8GB (2 x 4GB) DDR3-1333 Memory ($74.29 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ Amazon)
Video Card: Gigabyte Radeon R9 270 2GB Video Card ($209.99 @ Amazon)
Case: NZXT Phantom 410 (Red) ATX Mid Tower Case
Power Supply: Corsair CX 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($79.99 @ Amazon)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($20.95 @ Amazon)
Total: $733.43
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-02-06 19:23 EST-0500)

I've already bought all the parts, the goal was to keep it as low as possible, with a max of $800.

I also went with what was in stock as the time.

Will this work for my needs. What fps should I really expect?

For 800$ get these specs to run any game on max settings smoothly…
Here are the specs you need:
Processor - fx 8320
Motherboard - ga 78lmt-usb3
Ram - 8gb ddr3
Graphic card - r9 280x
Psu - 700 psu
Hard disk - 1tb
Cabinet - with onbuilt fan

You would get medium to high at least 50 FPS but would change the CPU.