600W is plenty for 3570K and most anything unless your going crazy with the hard drives and what not. I like to have at least 42 amps on the 12V+ rail for plenty of amps. Look for that in your PSU. I've had a 670 with my 600W PSU before (CX600V2). Would you also consider the GTX 760? It's cheaper and just very slightly less powerful (350 vs 250). Hope this helps!
PS. Depending on what GTX 670 you pick, that case will be long enough to support it. If you get Gigabyte's Wind force version of the GTX 670, It will take alot of space and may not fit. However, if you pick the reference models, they should fit no problems.