Here are two options, both are Lenovo G505s laptops using AMD's APU.
A10-5750m w/ integrated Radeon HD 8650g = $530
http/www.newegg.com/Product/Product.aspx?Item=N82E16834312829
A8-5550m w/ integrated Radeon HD 8550g + Dedicated Radeon HD 8570m = $500
http/www.newegg.com/Product/Product.aspx?Item=N82E16834312830
The difference between the two is the more expensive one has a more power A10 APU with the best performing integrated graphics core. The less expensive version has the slightly less power A8 APU with a less powerful integrated graphics core (iGPU), but it does have a rather weak Radeon HD 8570m which can "dual graphics" with the iGPU to provide better performance than either one alone. However, I have not seen any benchmarks that shows if the combine Radeon HD 8550g + Radeon HD 8570m is more powerful than the Radeon HD 8650g in the A10 APU.
Dual graphics only works with DX11 games. That means any games using DX10, DX9 or older will simply not take advantage of the Radeon HD 8570. There are also complaints about micro stutter by some people when using dual graphics. So this is something you should research more before you buy. If I had to choose I would go with the A10-5750m version so that I do not have to worry about micro stutter issues. Also, whether or not I play DX9 games or DX11 games the Radeon HD 8650g will be fully used.
The A10-5750m version comes with Battlefield 4 for free.
The A8-5550m version only has 4GB of RAM (vs. 6GB for the other one). This means it only has one stick of RAM which will affect the performance of the laptop because it will only be operating in single channel mode. When 2 sticks of RAM is installed the RAM will operate in dual channel mode. Single channel probably means around a 15% performance penalty.