No, it is not a good gaming rig. Also, does your $350 budget include the parts you listed? What type of games are you expecting to play?
Why is it bad? Tell me what I should do to make it better and I expect to play minecraft and games like TF2 and call of duty. I already have a PC and I will be using its case and power supply so I need 350 for the cpu motherboard memory and storage. I forgot to mention I will be using a asus radeon hd 6570 2gb video card.