not really hunting but i watched a show where an "modern day" Aztec threw a clay round bullet though a human skull...pretty powerful

If I had to hunt with a sling right now to put food on the table in an emergency situation I'd go down to the lake.  I that we're a coastal state here in New Jersey we always have lots of geese and ducks.  Though not considered to be very "sporting" I think that a sling could be best used shooting at flocks resting on the water.  Again, this is an emergency situation.  If you were handy with such a shot you could fire at them underhanded and even if your shot was a bit sort there should be enough power in the second or even third bounce to take out a duck of goose.  I have hunted ducks and geese with a 12 gauge shotgun before and I know how sturdy especially geese are.  Though I'm not mrboss, my shots are powerful and I'm sure that with a good hit I could knock a goose into next Thursday.  
  My second choice would be another very non-sporting way to hunt.  I'd wait until dusk and blast away at a squirrel's nest.  Though it would probably take me a few shots to hit one, the squirrels would stay put in the nest, believing that they are safe.  For this type of food gathering I'd use a longer sling for more power and a larger projectile, like around half the size of my fist, to negate any protection their nest might offer them.  
  I've got a long way to go before I'll be accurate enough to go into the woods and really hunt with a sling.  With that in mind, the sling could still be a useful tool for gathering food in some not so sporting ways.  Btw, in my state hunting with a sling, shooting water foul at rest on the water, and shooting squirrels in their nests are all illegal.  

Welcome, lone-star, and good post.  As far as stones go, I personally like slinging basalt.  It's very dense, usually round or oval shape, and packs a wallop.