Building a PC for a friend?

I've got a friend who's got an $800 budget. They would like to game on it, minecraft, DayZ, some newer games like BF/COD, etc. They will need a monitor, keyboard, and mouse also. I'm trying to keep it to where I can pickup the parts locally since they will be buying them and I will simply build the PC for them, this works out good since Microcenter has some of the best motherboard combo deals I've ever seen. 

I was thinking at least a 7870 w/ 4-8GB of RAM and an AMD CPU w/ 500-550 watt PSU. Probably a Fractal 1000 mATX case. I'd like to keep about $100 in there for labor, so the total build with the monitor, keyboard, and mouse should be no more than $700. In case you're questioning the $100 charge, I plan on doing full sleeving of the power supply, custom cabling, full wire management, etc. I don't intend on just slapping the machine together for them and hoping it works.

Any suggestions? Thanks!

$100 to build a friend a pc isn't that friendly. 

Quite literally, they are the ones who said they would give me $100 to build it. I did refuse the payment, but they won't accept that, so $100 it is. 

Have fun sleeving those cables.  I heard sleeving is a tiring and painful process lol.

http://pcpartpicker.com/p/25Htv

I wanted a fully modular PSU, but I couldn't get it as the price would kinda kill the budget(I don't count MIR in here).

btw, Source 210 only has one fan, so I picked up another one.  colors are somewhat matched, but there's no window, so it doesn't matter, unless you're willing to pick up the NZXT Source 210 w/ Window for about 10 bucks more.

http://pcpartpicker.com/part/nzxt-case-cas21w2b1

Sleeving isn't that bad for me, probably about 2 hours of work. I like that case just a bit better from the looks of it. Seems like cable management will be a ton easier in that particular case. I'll talk it over with them and see what they have to say about it. Thanks for the suggestion! :)

there's not really much point in sleeving when you're using a low end case, or one without a window. if i was you i'd just upgrade to an arc mini r2 or something :/ 

Hence is why I suggested the Source 210 Window!