I would recommend this latop. Acer with a Nvidia GT720m for 600 bucks.http://www.newegg.com/Product/Product.aspx?Item=N82E16834314178
Not a bad recommendation actually. I should have spent a few more minutes looking on Newegg to find that too lol. Technically, the HD 8650G is a faster and better performing GPU than the GT 720M. However, the HD 8650G borrows from the slow, DDR3 system memory while the GT 720M has its own, much faster supply of GDDR3 memory.
For the most part, this either puts the GT 720M on an equal or similar playing field as the HD 8650G or completely destroys it depending on the game, though the difference in performance can be really drastic depending on the game. For example, at 1360x768 on "high" settings, the GT 720M with the i3-3337U (the CPU that's included in the laptop linked by PsyKhiqZero) averages 44.2 fps. On the same resolution and settings, the HD 8650G with the A10-5750M (the CPU that's included with every HD 8650G) averages 45.7 fps. So in this case, the HD 8650G has a slight advantage.
However, then we look at a game like Saint's Row IV and the GT 720M's dedicated memory really makes a huge
difference. The HD 8650G with the A10-5750M at a resolution of 1280x720 on the "low" settings, the frame rate averages a laughable 11.7 fps meaning the game simply isn't playable unless you're willing to decrease the resolution a lot more. Then we look at the GT 720M with the i3-3337U at a resolution of 1360x768 on the "medium" settings and we save an average frame rate of a 29.9 fps. Clearly in that scenario, the GT 720M wins hands down in a major landslide victory.
:GT 720M benchmarksHD 8650G benchmarks
So overall, the GT 720M is a better GPU because of its dedicated memory, even if it just falls slightly behind in a few games, it has the potential to make a lot of games playable that would be unbearable on the HD 8650G. For $600, it's a good laptop.
Either will handle Minecraft very well. If you only want to play minecraft without a lot of graphical mods (HD texture packs, lighting effects, etc) then I recommend you go for the $530 laptop I recommended as it won't disappoint. If you want a gaming laptop that doesn't necessarily have a lot more performance in every game but has a wider spectrum of games available to it, then I recommend you go with the $600 laptop that PsyKhiqZero recommended. However, if you want a very capable laptop overall that can destroy most any game you throw at it at a resolution of 1366x768, then I recommend you go for the initial $769 Lenovo laptop I recommended.