Ok, you've made this much easier thanks!
This is an old machine, personally having just been upgrading my own AM3 machine, I would ditch it all and go for an i5 3rd or 4th gen, but I will answer your question. When I was upgrading my own machine I went for second hand motherboard and graphics as they are widely available at a good price - you'd get more bang for buck with such old components but the choice is yours.
Replace the motherboard with an Asus M5A series one, either the M5A97, M5A99 or if you need a micro ATX one then M5A-78L-M, there are a few varients of each of them, have a look which ones you like best. My favourite on a low budget for micro atx is the ASUS M5A-78L-M again of which there are a few with various features. I wouldn't go all out as the top boards only have things like better power for overclocking and Sli/crossfire which you dont need.
Spend what you like on RAM, I used 16GB in my board but you might be better saving money and just getting 8GB for gaming.
For the GPU then just get the top one for your budget, new that would be either a GTX760 or a R280 card, look for at least 2gb of RAM but more isnt too important for this build.
For a CPU I would get the FX6300 or FX8350 depending on budget (Im in the UK so your prices may vary to mine). If you just want a cooler the stock ones are fine, if you want quieter then the cooler master TX3 Evo and 212 EVO are both good value and perform well. The 8350 is the best for this socket (there are some silly 9xxx ones but avoid them - they are power hungry and need special motherboards) while the 6300 represents best value for money with a lower TDP
I do think though you'd be better saving up the full $500 and building a rig based on an intel h77/h87/h97 board and an i5 CPU