should this be a decent gaming setup for a 350 dollar budget I already have a hard drive for it

Solution
Much better choice:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($77.99 @ Newegg)
Motherboard: Gigabyte GA-F2A55M-S1 Micro ATX FM2+ Motherboard ($44.69 @ Newegg)
Memory: Crucial Ballistix Sport 4GB (1 x 4GB) DDR3-1600 Memory ($35.99 @ Amazon)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($34.99 @ Micro Center)
Power Supply: OCZ ZT 550W 80+ Bronze Certified Fully-Modular ATX Power Supply ($54.99 @ Amazon)
Other: HD 6970 POWERCOLOR - CLICK TO SEE NEWEGG LINK ($104.00)
Total: $352.65
Prices include shipping, taxes, and discounts when available
Generated...

RazerZ

Judicious
Ambassador
Much better choice:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($77.99 @ Newegg)
Motherboard: Gigabyte GA-F2A55M-S1 Micro ATX FM2+ Motherboard ($44.69 @ Newegg)
Memory: Crucial Ballistix Sport 4GB (1 x 4GB) DDR3-1600 Memory ($35.99 @ Amazon)
Case: NZXT Source 210 (Black) ATX Mid Tower Case ($34.99 @ Micro Center)
Power Supply: OCZ ZT 550W 80+ Bronze Certified Fully-Modular ATX Power Supply ($54.99 @ Amazon)
Other: HD 6970 POWERCOLOR - CLICK TO SEE NEWEGG LINK ($104.00)
Total: $352.65
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-22 23:39 EDT-0400
 
Solution
OPTION BUILD

PCPartPicker part list / Price breakdown by merchant

CPU: AMD A8-7600 3.3GHz Quad-Core Processor ($104.99 @ Newegg)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($69.97 @ NCIX US)
Memory: Crucial Ballistix Sport 4GB (1 x 4GB) DDR3-1600 Memory ($35.99 @ Newegg)
Video Card: MSI Radeon R7 250 2GB Video Card ($79.99 @ Newegg)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($39.99 @ Micro Center)
Power Supply: Antec 450W ATX Power Supply ($34.99 @ Amazon)
Total: $352.92
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-23 00:09 EDT-0400

this system should be a hybrid crossfire, with kaveri technology they can work with R7 240 & R7 250 with ddr3/ddr5 memmory. I picked r7 250 for maximum potential hybrid crossfire, I changed your ram in to 1600mhz, you really cant see their difference in this low type of rig, I picked antec vp 450 for hi quality atx standard, I picked the cm haf case for the best airflow case on your budget

http://www.pcper.com/reviews/Graphics-Cards/AMD-A8-7600-Kaveri-APU-and-R7-250-Dual-Graphics-Testing-Pacing-Fixed