Ah, sorry about that. I typically go on a copy and paste spree and never really bother to explain why, lol.
Well, a 500w PSU will handle a modern CPU + single GPU setup. You also want to make sure the PSU is 80+ certified as well as manufactured by a reputable company. Seasonic, XFX, Corsair, Antec just to name a few are among some of the most reliable brands.
As for the GPU, I chose the HD 7950 simply because your budget could handle it. I'm not exactly sure what games you'll be playing, but this thing can handle Battlefield 3 on Ultra at 60 fps at a resolution of 1920x1080. It's a beasty graphics card with huge overclocking potential. If you're an nvidia fan, feel free to switch this out for a GTX 660 Ti or a GTX 670. You could also switch this out for a HD 7870 if you feel that this is too much power for your needs.
As for the case, I just chose something that looked aesthetically pleasing and had decent airflow. The HAF 912 easily meets those standards and then some. It's fairly spacious and can hold all your components. If you want a different case, feel free to change it. This is a personal decision, and you should take your time making this decision since you will be the one that has to stare at this machine each and every day.
I chose 8gb of RAM simply because anything more is overkill. Games barely use up 4gb of RAM these days. 16gb of RAM is used more in things such as video editing/rendering. If you feel you're budget can handle it, go for 16gb. You won't notice a performance difference in games though.
Also, I highly recommend you grab an aftermarket heatsink. Overclocking can easily net you a 15-25% boost in performance...possibly even more. Besides, the cooler is only a mere $30. If not for overclocking, you can at least do your computer the favor of ditching those shitty stock coolers that are packaged with the Intel and AMD CPUs. The Hyper 212 Evo will keep your CPU much cooler.