What makes for a good gaming desktop?

I have recently realized that my laptop (although fine for minecraft) is not good enough to run more complex games such as Skyrim, Arma II, Fallout, ect. My current setup is 6 GB of RAM and some low grade graphics card. Some have even told me I don't have a graphics card after checking my computer although I can run minecraft at 10 - 30 fps so I would assume I do have some form of card. I'm fairly clueless as far as knowing what to look for and have a budget of 500$ does anyone have any suggestions or advice?

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