As the beef in this recipe is braised over several hours, you need a cut of meat that is suited for long and slow cooking times. Silverside and topside are great cuts to go for as is rump or skirt steak.
You might also see steaks labelled as braising steak or casserole steak in your local supermarket. This is the generic term for any type of beef which is suited to slow cooking so will work well for this recipe (as long as it isn't pre-diced as you need full steaks for this recipe!)
There really is no need to splash out on expensive meat for this recipe. The slow braising will transform a tougher cut into a meltingly tender piece. However, make sure that you choose pieces that don't look gristly because no amount of cooking will fix that!