So, I think you'll have better luck if you give some info about what you want to play and the settings on which you want to play it. A 300-400 dollar machine isn't going to be able to play much on max settings - probably nothing current. But maybe you don't care much about that.
Then, I wouldn't build it. I think that unless you buy used parts, at that price point, you are going to have better luck buying from something like cyberpowerpc or the like. That way, you can take advantage of their volume pricing and any deals they have running.
I was just speccing out their cheapest model - based on an i3 and I got it specced out at $550 with an nvidia 750ti and a 400w evga power supply. I stepped down the mobo and I skipped the optical drive. I'm no master builder, but it strikes me that it would take a master builder to build a computer that can actually play recent games, on low to medium settings, for around 300-400 dollars.
Good luck!