Which cuts of beef are suitable for slow cooking methods?
Beef for Slow cooking methods:

When shopping for beef that will be cooked long and slow, price per pound within a grade will be a helpful guide. Less tender cuts that will be best cooked long with liquid will be much less expensive than the naturally tender cuts that require less cooking i.e. filet mignon.

From http://life.familyeducation.com/


  When shopping in the supermarket for meat destined for your slow cooker, here are the cuts to look for: 
  
  Shanks - Shoulder - Round - Rump
  
  Even if they are not labeled as such, you'll know you've selected the
  proper slow cooker cuts when you compare the price of these cuts with
  cuts such as tenderloin, sirloin, and rib. And there is no need to go
  for the high-priced Prime grade meats. Choice and Standard quality are
  just fine.


To visually find the right cuts of beef for slow cooking look for:


Multiple muscle groups within the cut. In between each muscle is where you find the connective tissue that will break down. This shank has several.

Course grain is found in the working muscles of the animal. You can see the long fibers in this flank steak.

Fat - good marbling within the cut, but not too much on the exterior, like this pot roast.

A great guide to beef cuts can be found at chefsteps.com