for mountaineering, where you're just on snow and ice and not hitting anything techical, a half rope is often nice and light and perfectly strong enough... but, beware,if you're dragging it over lots of sharp rock or will hit any real technical climbing, a light single rope's probably the best (9.2-9.8 ought to be fine). half ropes also suck sometimes for prussiking and they stretch a heck of a lot too so some would argue they're not the best for glacier travel.