HP H8-1214. GPU and PSU upgrade for son for Christmas

Hi
I bought my son a HP H8-1214 in the summer. Not knowing much about computer gaming, I understand this computer's performance could use some help.

Games he plays on the computer:
My son plays Minecraft and some other various PC games. He does not play WOW, Skyrimm or BF3 on the PC. With the exception of WOW, he plays COD, BF3 on his Xbox 360. He seems content to stick with the 360. His big PC game is Minecraft, I'd say at least 90% of his PC gaming is Minecraft.

I can't see going out and buying a new computer, can't think of what I would do with the HP and know resale would be quite the wash. ( wish I would have known more when I bought it )

After doing a lot of reading here, I do see others have upgraded their HP H8-1214 and they express satisfaction with doing so. However I have to admit a lot, errr, most of the spec talk goes over my head. Thus I am pretty clueless at this and would appreciate any input.

Here's the tentative plan
A Corsair Enthusiast Series 80 plus bronze modular 650M PSU with a GeForce GTX 660.
http://www.amazon.com/gp/product/B005E98I0G
http://www.amazon.com/EVGA-GeForce-SUPERCLOCKED-Graphic...

Searching here, people report having 10 inches within the case and this graphics card is 9.5. Is that okay or am I cutting it too close?

Also after reading about the card, I am wondering about cooling and if anyone can report how much of an issue that would be with this card in this case. If it is an issue, can I buy a fan? Any suggestions on one of needed?
Or should I just go with another graphics card?

What is your general opinion on this plan? I want to make the upgrade worth its while and would like to stay below or in the low $400's if possible.

Thank You
A Clueless Mom