To be honest, you'll probably find that the vast majority of full tower cases would support 6 or more HDDs. Likewise they would more than likely be large enough to accomodate full length graphics cards such as those you mentioned. A few examples though in no particular order:
Coolermaster HAF932, Coolermaster HAF X, NZXT Phantom, Antec 1200, and obviously Lian Li's full tower cases. Be sure to double check they have the required number of drive bays etc beforehand though since these are just off the top of my head.
As far as PSUs go, again you'd be better off checking individual PSUs for connectors first but I'd say a solid unit around the 600W-700W range would do you fine. Recommended brands are Antec, Corsair, Seasonic etc.http://www.jonnyguru.comhttp://www.hardwaresecrets.com
are the places to start looking for PSU reviews.