Good advice again from Biz. Get a Seasonic or Cosair PSU, you can get one for 100$ for what you need. Regarding the case if you choose to build, I recommend finding a deal on a Corsair case. I've used many types in the last 2 years, and they've always been among the better, if not best. I found a C70 case, on of their new ones, for 75$ on sale, regular 140$. I actually prefer it over my d650 and d800 cases, one of which is 300$. It has the best cooling and circulation I've found in a sub 100 dollar case, and cleanable removable air filtersx3 in it. It's solid as a tank, with rubber carry handles on the top in order to move it around easily, something most cases do NOT have. I can help you find it cheaply if you want as well, PM me any time.
The advice on the 3570k or not k is pretty decent, however I recommend overclocking the K, it'll really give you the best value with almost no risk with a decent air cooler. I recommend air too btw, I know so many guys that say go with the corsair 60 or 100 water coolers, but I still do not trust them, and most builders don't give you a system warranty if you put one in, so draw your own conclusions from that. (I'm talking memexpress, ncix, etc up here in Canada, I'm not sure about US builders on this score). I'm using a Noctua D14 for the socket 2011x79 platform with an overclocked 3930 chip that's at 4.6, and never once had it lock or fail me. It even runs at the same temp as what the factory non custom water guys are getting (ie the corsair or whoever brand sealed h2o units). That all said, a 3570 without the k will run most of the cards up to their potential in your price range, you'll just lose maybe 10-20 percent on the frames per second on some games, it'll vary greatly, some you may not see any difference at all. Either way, have fun. I would take that advice about that system you suggested RPM, that video card just won't cut it for long imo. I had a 7770 in my old i7 920 box, and it couldn't run AH2 at anything near max, but it would get by ok with some stuff turned off. It also "got by" with every game out there, but getting by won't cut it for long. Any 600gt class card is a very cheap card, if you pick any of those systems at least get the 7770, but for your money you can do SO much better.