I advise you to avoid any laptop with an AMD E series APU like the Lenovo G575 43834WU. They are very weak; even the newer generation E2 series are weak.
If you don't mind a 17.3" laptop then consider one of the following for $400 from Bestbuy. However, you need to add taxes as well.
HP - Pavilion 17-e110dx - Quad core AMD A8-4500m APU (1.9GHz / 2.8GHz) with Radeon HD 7640G
http://www.bestbuy.com/site/pavilion-17-3-laptop-4gb-memory-750gb-hard-drive/3215015.p?id=1219089114771&skuId=3215015&st=categoryid$pcmcat247400050000&cp=2&lp=14
HP - Pavilion 17-e019dx - Dual Core Intel Core i3-4000m (2.4GHz) with Intel HD 4600
http://www.bestbuy.com/site/pavilion-17-3-laptop-4gb-memory-750gb-hard-drive/2854029.p?id=1219079079760&skuId=2854029&st=categoryid$pcmcat247400050000&cp=3&lp=3
Those two laptops from Bestbuy's website offers the best gaming performance. While the AMD APU has 4 cores each core is a bit weaker compared to each core in Intel's dual core CPU. There's roughly a 30% performance difference so a Haswell generation Intel CPU running at 2.4GHz will be equal to an AMD APU running at 3.1GHz. AMD's CPU has two speeds 1.9GHz is the "normal" max speed, but with Turbo Core (TC) it can reach 2.8GHz, but only when one CPU core is used. The more cores used the lower the max speed. I would guess 2.6GHz for 2 cores and 2.4GHz for all 4 cores. TC is basically an auto overclock.
People will generally tell you that AMD's graphic cores are better than Intel graphic cores. That is generally true, but it also depends on what specific models you are comparing. There are currently only two Radeon HD graphic cores that outperforms the Intel HD 4600. They are the Radeon HD 8610g and HD 8650g. The Radeon HD 7640g is closer to the performance of the Intel HD 4400 which means it is less powerful than a nVidia GT 620m / GT 525m and the Radeon HD 7610m discrete graphic chips.
Of the two HP laptops, the Intel version will offer you the best performance because the CPU is stronger. Minecraft and most games in general only use 2 CPU cores. And because the integrated Intel HD 4600 graphics core is more powerful than the integrated Radeon HD 7640g graphics core.
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