As far as the case goes, pretty much any ATX mid-tower would be able to fit your 4 drives...and you could get some adapters (brackets or hot-swap drive bay adapters) to stick more in the unused 5.25" external bays. The rest is just up to your aesthetic preferences and budget.This Lian-li mini-tower
could work for 4 drives + dvd/blu-ray
A case that is designed for a bottom-mounted psu might be a good idea.
Pretty much any decent modern video card should be able to handle 2 1080p60 displays. More often than not, the smooth playback portion of things will come down to your cpu rather than the video card. A nVidia GTS 250 (or better), or ATI HD 3850 (or better) should be more than enough. Cards newer than that should have good enough hardware acceleration for decoding H.264 (and mpeg2 acceleration shouldn't be an issue). Getting your setup to use the H.264 acceleration is another story though. IIRC, it pretty much means using DXVA on windows or XvBA on Linux.
A word of caution, some mid tower cases (like my x-cruiser
) will only be able to accommodate a 9.5" (~24.2cm) card. It depends on how the HDD cage is oriented and the location of the video card's power connector(s).