GTX 650 With which processor?

I'm passing over my old graphics card (ASUS GTX 650 1GB) to my younger sister.
I'm looking at two different processors at the moment.

AMD Athlon ii x4 750k 3.4GHz, 4MB Cache, (4 Core, Socket FM2, 100W) = £56

OR

AMD A8 5600K (3.6GHZ, 4MB Cache, 4 Core, HD6570, Socket FM2, 100W) = £64.50

I'm curious as to which one will be better?

Will the A8 give a boost to gaming? Or will it cause problems (compatible issues possibly?)
She won't be into hardcore gaming. Mainly stuff like Minecraft, Terraria, Starbound etc. But she may want to try games like skyrim out and i'm curious as to whether the APU would give a lil boost of frames.

I'm on a really tight budget building a PC for my sister, so please don't recommend other processors.

If I do get the APU I will be getting a 8gb (2x4) 1600mhz ram. I heard though that 2400 mhz are more suitable for this type of processor though.

With an Nvidia card present, the GPU portion of the APU will be inactive, so it wouldn't make a difference.

Also the A8 5600K has a Radeon HD 7560D GPU intergrated. The HD 6570 is a discrete card.

The 750k is probably the more logical choice.

" I do get the APU I will be getting a 8gb (2x4) 1600mhz ram. I heard though that 2400 mhz are more suitable for this type of processor though."

Again, only really matters if you're using the intergrated GPU, which you won't be.