If you're willing to spend just a little bit more, about $20 over your budget, you'll have a MUCH BETTER, system. Many people think that Bulldozer/Piledriver sucks *** balls, but they're quite wrong.
My build here:
http://www.squidoo.com/electronicandmore#module146695821
Now let me explain, the FX-6300 in my build is much better than the i3 3225, I will tell you right now, much better especially in multi-threading and in gaming like BF3 you won't really see the difference. Any high-end game requiring heavy GPU, the CPU matters less than the GPU.
Here's the proof:
http://www.hardwareheaven.com/reviews/1598/pg6/amd-fx-8350-processor-review-battlefield-3.html
As you can see, at 1080P, the FX-8350 performs AS well as a i5 3570K, I use this comparison because many people say that the FX-8350 is utter crap.
Another example: http://www.legitreviews.com/article/2055/6/
Again: http://www.legitreviews.com/article/2055/7/
Again: http://www.legitreviews.com/article/2055/4/
Wifi cards aren't expensive at all they're just about $20 for a usb wi-fi adapter.