For $800 I'd really hesitate to recommend a case that cheap (nothing against NZXT though), and do not use a 5900 RPM HD as your primary - that will be a major bottleneck. You want a 7200 RPM or an SSD as your primary to avoid lag time as much as possible.
The NZXT case will fit the cooler. It is actually a really good case. I would try to find a 7200 RPM HDD however, the Caviar Green will be quite slow. (Caviar Blue or a drive from another manufacturer)