All you really need is a good Graphics card. Like a Geforce or Radion that has 512mbs of video RAM or more to play minecraft at its best. I know because i used to use a 1999 personal computer with a single-core 1.9ghz processor and only 1gb of system RAM and it had some old AGP Geforce graphics card with 512mbs of video RAM and it could run minecraft on far. LOL So just make sure what your getting has a good graphics card in it, like one that has 1gb of video RAM. minecraft really doesnt take too much to run.
So if your getting a new computer then it most likely uses pci-e for graphics, or just it being a computer 2010 or newer you shouldent have to worry too much on running minecraft.