Hello, this is the laptop that is best for you.
http/www.newegg.com/Product/Product.aspx?Item=N82E16834314119
It is out of stock right now, but it is by far the best laptop you can get at around $500.
Going up to $600 gets you pretty much the same system with better CPU.
Going up to $800 gets you a much better computer all around.
However, at $500 there isn't any laptops that have even close to the CPU and graphics performance. No laptop under $600 can match it in graphics performance, and only a few match it in performance up to the $750 price point. A few laptops have a little bit better CPU performance under this price, but they are way lower in graphics performance. I completely recommend this laptop, no matter how much you look around online I know you will not find a better one at this price.