With a budget of $550, you can do better than an APU system. You said it didn't need to be pretty right? A $30-$40 case will work just fine. You also don't need to buy an $85 PSU. A nice $45-55 one will work well.
Basically, with a $550 budget, that is enough to afford a decent discrete video card. That APU will play the game, but if the only reason you're building this system is to play it, the whole idea should be to get the best video card you can with your budget, while toning down crap that doesn't matter -- like the case and a more expensive PSU than you need. There are plenty of decent quality/brand ~500 watt PSU for a hell of a lot cheaper than $85.
Also, going with a discrete video card later on with an APU system sort of defeats the purpose of buying it in the first place. I'd rather get a discrete video card the first time around, rather than half-assing it for awhile, and then giving my APU system the finger.
The secret to compiling a build list for someone with a budget is to cut costs wherever it won't hurt them, and then spend that money on crap that actually boosts performance. Not spending extra for a "super-sweet" $85 Corsair v2 PSU just because someone has a psu fetish and that this way, they'll be "set for sure and now their system REALLY won't blow up!"