If you are going mini-itx, intel is the way to go 99% of the time.
although the cpu you selected is not compatible with any mini-itx mobos, I figured I would stick to amd for you.
I chose the AMD Athlon II X4 750K. A bit old, but it will do the job.
http://pcpartpicker.com/p/2hUOJ
EDIT:
I chose the evga because it is a blower style card, which will help alot with the cooling in this case
I didnt include an OS, as going linux would give you better specs for the price.
If you want to go windows, try this.
http://pcpartpicker.com/p/2hVec
(this has a worst processor, graphics card and less RAM)
EDIT:
If you are wondering why I chose 1 stick of 4gb RAM, it is because although 2 sticks of 2GB would be slightly faster, the difference wouldnt be much, and I feel the option to upgrade with another 4gb ram stick to make 8gb in the future is worth a lot more.
Ultimately, 500 bucks is a bit hard for a mini-itx gaming build, just 75 dollars more would give significantly better performance. Also, not going intel is also a bit harsh.
That being said, I hope I could help.
If you are really on a budget, get a normal size computer, you will get better performance for your budget.
If you must have a mini-itx build, try to save a few more bucks.
That being said, my build will be able to play the most graphics intensive games well at low-medium settings, and if you are ok with that, then you might be happy with these builds. You definitely wont be wow-ed though, and if you are like most people, you will be thinking about upgrading within less than a year... Unfortunately, almost everyone in this world wants more than they have.
I should also mention that I am concerned about cooling on this build. Although I think you will be fine as is, make sure you keep this in a well ventilated area, and to try to keep the room as cool as possible on really hot days.
Also make sure to clean the interior of dust every so often.
Anyways, Good luck finding a rig that fits your needs, I hope I helped!
EDIT:
here is an intel build (sorry for going slightly over your budget):
http://pcpartpicker.com/p/2hVPh
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