ATM, high end APUs are overpriced and not suitable for a $400 budget. The recommended low-end intel+dgpu setups will likely perform better in the majority of games, and will be suitable to upgrade should your friend decide to aim for something better.
Here's something around $400 that will perform well out the gate. A better PSU that could handle a solid GPU upgrade is $10 more(CX430), another $20 or so could make that 750 a 750Ti, but as is, it's good enough for 720p.
god invented extension cords. -elchris79 Starcraft 2 has no depth or challenge -GoreGross
Can't OC it, but is that really a necessity for the performance they'd be looking for out of this (it will run anything at 1080p barring adjustments to settings or AA). Could even spare some money going with 4GB or RAM and upgrading to more later, or adding higher storage, etc. now.
Shub's was also a good one, a couple similar parts but trade-offs for the OCing of the CPU and more expensive mobo but less RAM and standard HDD. Guess it depends on what they can make do with now or if they have alternative storage options (a removable HDD, SD card/reader, thumb drives, etc. for media or such).
Also, could opt for a $5 more Asus mobo with USB 3.0 onboard.