CPU: AMD A10-7850K 3.7GHz Quad-Core Processor ($129.99 @ Amazon)
Motherboard: Biostar A58MD Ver. 6.x Micro ATX FM2+ Motherboard ($41.36 @ Mwave)
Memory: G.Skill NS Series 4GB (1 x 4GB) DDR3-1600 Memory ($36.99 @ Newegg)
Storage: Toshiba Product Series
T01ACA 500GB 3.5" 7200RPM Internal Hard Drive ($41.99 @ NCIX US)
Case: Rosewill REDBONE U3 ATX Mid Tower Case ($24.99 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Newegg)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($12.99 @ Newegg)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($89.98 @ OutletPC)
Wireless Network Adapter: TP-Link TL-WN725N 802.11b/g/n USB 2.0 Wi-Fi Adapter ($8.07 @ Amazon)
Total: $406.35 (USD)
For the most part, an A-6 can run minecraft around 40 fps.
A10 shouldn't have any trouble running minecraft, but don't expect to run any heavy games (etc. Battlefield 4, COD AW, etc)