The APU is an AMD cpu with the gpu attached directly to it in the same package. a 4 core apu is going to perform approximately the same as a 4 core cpu only having the graphics performance of a low-midrange cpu. The APU also heavily relies on the memory speed where it is not quite as apparent with the cpu as the apu uses the system memory to power the graphics. Low end Machines are ideal for these apu's
The 400 dollar machine I built for you in your last thread will absolutely have no issues with mine craft or running it and acting as a server. Seriously go back to that thread and build what I provided I assure you there will be no complaints. It can also be overclocked both the cpu and gpu on the apu are overclockable.
Also please note the APU I provided is the fastest available and can use 2400 ddr3 ram, I only provided 2133Mhz ram so upgrade that if you like my build was under 400 dollars
http://www.newegg.com/Product/Product.aspx?Item=N82E16820226545