I'm going to murder you, necro posters.

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.

there are my specs for my desktop:

RAM: 4.00 GB Dual-Channel DDR2 @ 199MHz

CPU: Intel Pentium Dual Core 820 (2.80GHz)

Graphics: nVidia GeForce 9500GT 1gb

I have 2gb RAM dedicated to Java and it runs smoothly on full settings, though if your laptop only has 2gb ram don't do that for obvious reasons it depends really, like ewok12 said, what else are you going to be using it for?

Well the minimum RAM i've been able to run MC on is 512.... But thats on the lowest for everything, My main computer I've custom built to have a terabyte of RAM and that seems to run it pretty well.... xD
Other than that its just personal preference, about what precisely your using you computer for!!! xD