Acer Aspire S3-391-6497 13.3-Inch Ultrabook is the best laptop for you in 600$. Its processor is Intel core i5 with 4GB of Ram DDR3 and also with the hardware of 500GB 5400rpm with intel HD graphics 4000. Its operating system is Windows 7 home premium 64bit.
It totally depends on you that what type of games you have to play on the laptop, either its heavy games or a small games. For that you can take a laptop with your satisfied specifications