The HP Envy with the AMD a8 is a good bet. I own one with an A10 APU. It is thin, sleek, metal, has great gaming performance, and within your budget. It is a little noisy, and the keyboard has some flex though. My only upgrade would be to get the 1080p screen.
http
/www.shopping.hp.com/en_US/home-office/-/products/Laptops/HP-ENVY/E1U67AV?HP-ENVY-15z-
j100-Notebook-PC-ENERGY-STAR-
Watch my vid on it.
http/youtu.be/JpeF-MfRrUg