I second the link. This website has a competition every month to determine the best way to spend $500 on a computer and it is judged by real experts not people paid by companies to push products.
You probably cannot possibly do better than the one in the link for regular everyday use and reasonable gaming.
If the kid wants to play the best games with ultra awesome graphics and stuff, it just won't happen with $500.
Still, $500w will buy you reasonable graphics with new games which is all you can really ask for. The one in the link will give you that probably better than any other way to spend the same $500.