I Need Everyones Help

I would like to buy my sister a pc but i cannot decide on what should be in it.
I came here today to ask for everyones help or more so opinions on builds.
Does not have to be very powerful. Just good enough to play minecraft on with little to no lag and handle small gaming graphics.
I'm not looking to spend much but if it works i'll consider it.

Thanks a lot everyone its very appreciated. 

this is a decent little APU based build - http://pcpartpicker.com/p/1WzV4 

however, if she becomes interested in the thousands of other pc games that are out there, she might want to invest in a good GPU (if she wants the games to run well). but for just minecraft, what i've set up will be just fine. 

I would upgrade to 8GB.  Also, the prodigy is HUGE for a mini itx build.  Try this:

http://pcpartpicker.com/p/1WA2e

And yeah, ck3's advice is pretty good.

how can you call the Prodigy huge when Mini ITX is the biggest motherboard form factor it supports? xP and bigger means better airflow - anyways, the node is pretty good and the dual channel 4 gigs was just to hug the budget a little tighter.

I meant compared to other cases.  The Prodigy M is basically the same size, indicating how bit the Prodigy is.

http://pcpartpicker.com/p/1WBKx a very upgradable build. The motherboard will support the upcoming amd FM2+ series CPUs and the GPU is great for the price but if you can find a hd 7770 or something similar that will fit your budget and get the free games with it that would work find to. If you or her want to overclock or thing you will want to go to the 750k its about 15usd more but for overclocking it will be great and for the storage (as i dont know how much she will you) i only put in a 1tb but for about 20usd more you can get a 2tb. And yes i know its a stupid case but i have one and its great, it has everything you need and thats it.

It's upgradeable, but pretty weak to start off.  If you wanted to upgrade the GPU, the R9 250 will be pretty hard to sell.

its cheap bro. lol cheap is cheap any way you look at it. he gave no budget and said it had to be low cost so thats what i did and for minecraft you dont need 4 way titans and a 3960x lol.