Intel or AMD build

Solution
The i3 is not a very good gaming CPU. If you save save the extra bucks for a low end i5. If you are on a strict $400 budget get an A10 system, if you can spend a bit more an Athlon X4 860K + R7 370.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.89 @ OutletPC)
Motherboard: Gigabyte GA-H97M-D3H Micro ATX LGA1150 Motherboard ($74.98 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($46.88 @ OutletPC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($52.33 @ OutletPC)
Video Card: Sapphire Radeon R7 240 2GB Video Card ($60.98 @ Newegg)
Case: Cooler Master N200 MicroATX Mid Tower Case ($43.99 @ SuperBiiz)
Power Supply: SeaSonic 450W 80+ Gold Certified ATX Power Supply ($59.16 @ SuperBiiz)
Total: $403.21
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-18 19:08 EDT-0400
 


This is the best I could come up with (http://pcpartpicker.com/p/7vZhHx) around $40 more than your price point, but a lot better, IMO.
 


No offence, but that video card is pretty low.
 
PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($70.89 @ OutletPC)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($60.89 @ OutletPC)
Memory: Corsair Vengeance 8GB (2 x 4GB) DDR3-1600 Memory ($41.99 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($52.33 @ OutletPC)
Video Card: Sapphire Radeon R9 270X 4GB Dual-X Video Card ($168.99 @ SuperBiiz)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply ($34.99 @ NCIX US)
Total: $430.08
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-10-18 20:52 EDT-0400