Preferably all copper, BUT be very carefull, those things weigh half a ton (actually around 775g), and can damage your omoboo if jostled. Try and find one that gets good reviews and falls within AMDs limits on weight.
The (all copper) HS's are very heavy, but if installed properly it's not a problem at all. Just don't drop the MOBO off the table with the heatsink installed. Then you'll be all set.
If you want the best cooling then all copper is the way to go. But if you want a little cheaper/less heavy then just a heatsink where the contact area is copper and the fins are aluminum (that will do fine). Like a zalman Al-cu version or something. Because the contact area is still copper but most of the fins are aluminum so not much cooling is lost. I saw the differences in a review and there is very little difference between the all copper and the al-cu (for zalman anyway).
If you are referring to the 7700-cu you do not need a special case. It fits fine in my standard ATX case. Usually the only problem is that it somtimes obstructs the first two ram slots. But you can always install the ram first or use only the 3 and 4 slots.