Best build for 500$

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6350 3.9GHz 6-Core Processor ($129.94 @ SuperBiiz)
CPU Cooler: Cooler Master RR-HT2-28PK-R1 54.8 CFM Sleeve Bearing CPU Cooler ($16.99 @ Amazon)
Motherboard: ASRock 970 EXTREME4 ATX AM3+ Motherboard ($74.49 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.98 @ OutletPC)
Video Card: Asus Radeon R9 270X 2GB DirectCU II Video Card ($179.99 @ NCIX US)
Case: NZXT S340 (White) ATX Mid Tower Case ($69.98 @ Amazon)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($44.99 @ NCIX US)
Total: $646.35
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-07 09:37 EDT-0400

I could only get up to 600 dollars for this.

I know it's only 100 dollars more, but I have taken into account video editing and you will need alot of cores to handle this.

or this strong CPU and is more than capable of your task.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4430 3.0GHz Quad-Core Processor ($177.27 @ TigerDirect)
CPU Cooler: Cooler Master RR-HT2-28PK-R1 54.8 CFM Sleeve Bearing CPU Cooler ($16.99 @ Amazon)
Motherboard: ASRock B85M Pro4 Micro ATX LGA1150 Motherboard ($69.99 @ Newegg)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($74.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($54.98 @ OutletPC)
Video Card: Asus Radeon R9 270X 2GB DirectCU II Video Card ($179.99 @ NCIX US)
Case: NZXT S340 (White) ATX Mid Tower Case ($69.98 @ Amazon)
Power Supply: EVGA 600B 600W 80+ Bronze Certified ATX Power Supply ($44.99 @ NCIX US)
Total: $689.18
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-07 09:39 EDT-0400
 
Solution


Radeon is great for hardcore gaming, since you stated you wanted "HARDCORE" gaming I got you a high end GPU for your tasks. And two great systems for your Video Editing. Of course as the man above this post stated we did not include the OS.