This is what I got for you FX 8350 build since mine was premade on pcpartpicker. it's about $35 over budget but you can choose to get a more cost effective chassis if you don't like the Fractal Design. The Cooler Master HAF 912 is a builder classic and it comes in at about $60. I would try to keep the Fractal Design though.
By the time summer comes a lot of these prices will be different. If you are planning to build it then just save your purchase till you are about to build it and buy the parts at one time. So this is just generally a guideline for you and pcpartpicker is a great tool to narrow down your hardware list.
When summer comes there will be different parts and different prices. anyway good rule of thumb to use when making a gaming rig is to put more money in GPU than in the CPU or at least the same amount roughly. Also unless your going for huge overclocks downgrade the MB and save some cash there. 1600 mhz memory is fine you won't notice the difference in speed unless your using a APU. A aftermarket CPU cooler is not necassary for a gaming rig again unless yor gonna overclock. You can save a considerable amount of money and have a computer that runs games at a equally high level if you cut out some of the "easy picks" of parts everyone uses.