Without including low quality cheap parts such as Corsair CX PSU, this is the best I can suggest with that budget.
PCPartPicker part list:
http://pcpartpicker.com/p/TBD2yc
Price breakdown by merchant: http://pcpartpicker.com/p/TBD2yc/by_merchant/
CPU: Intel Core i3-4130 3.4GHz Dual-Core Processor ($113.99 @ SuperBiiz)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($42.89 @ OutletPC)
Memory: Kingston HyperX Fury Black 4GB (1 x 4GB) DDR3-1600 Memory ($22.69 @ SuperBiiz)
Storage: Seagate Barracuda 250GB 3.5" 7200RPM Internal Hard Drive ($21.95 @ Amazon)
Video Card: Asus Radeon R7 260X 2GB Video Card ($92.98 @ Newegg)
Case: Apex TM366BK MicroATX Mid Tower Case w/300W Power Supply ($19.99 @ Directron)
Power Supply: Antec High Current Gamer 620W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ Newegg)
Total: $374.48
Prices include shipping, taxes, and discounts when available