Unless you want deticated graphics i dont think you would be able to have a good computer for around 350 while paying that much for a mobo heres what i think you should use:
Cpu: AMD Athlon II X4 740 3.2GHz Quad-Core Processor
Mobo: ECS A55F2-M4(1.0) Micro ATX FM2 Motherboard
RAM: Corsair 8GB (1 x 8GB) DDR3-1600 Memory
GPU: Gigabyte GeForce GTX 550 Ti 1GB Video Card
Case: Apevia X-TRPJR-BK/450 ATX Mid Tower Case w/450W Power Supply
Total Price: $353.93