I would've get a 3570K and a CPU cooler so that I can overclock it (only if you're into overclocking). If you're not, then you could save a couple bucks by buying an H77 or B75 motherboard (depends on what you need). Also, a 3470 performs almost equal to a 3570, so you could also save a few bucks there.
My rule of thumb is to always buy an aftermarket CPU cooler because I believe Intel stock coolers are terrible (loud and those plastic push pins, ugh). Get a cheap CPU cooler like a CM Hyper TX3 or Hyper 212+. But really, this is just me and it will be fine if you don't care about it so much. If you want to overclock though, it becomes a necessary and coolers I recommend are (from least to most) Hyper 212, Scythe Mugen 2, Thermaltake Frio and Noctua NH-D14.
That's not the case that I would choose, though as long as it has enough vents and supports your motherboard, video card and coolers, it'll be fine. How much is the price of that case anyway?