A David and Goliath type sling. It is really fascinating. There are about a million different ways to throw, helecopter, figure 8, Byzantine, Apache, the list goes on and on. I'm going with Apache which seems to suit me, and is a pure hunting style. As opposed to a war style.
A hunting style is all about stealth, a war style is all about power.

Loosely translated, my projectile at 1500 grains, going about 200fps is about as powerful as a .22 rim fire. A good shot can kill animals up to deer and sheep.

Accuracy is the trick though. I really can't think of anything that average people do that takes as much skill and muscle memory. When I started I would say my groups were maybe 20ft, at about 20 yards. My groups are now down to about 5 feet at 20 yards. So I still don't have any usable accuracy. But I know people who can knock apples out of a tree by hitting the stem, so it is possible.

I still have a much better chance with a throwing stick, and so that is what I will be hunting with very soon. But the sling has WAY more potential, I think.
Rocks are easily my favorite projectile. But consistency is very important for accuracy. So it takes a lot of time to find just the right rock. That's fine for hunting. Spend 30 minutes picking 3 good rocks, and go hunting. But it sucks for practice. Back in the day of war, they used hardened clay balls for projectiles, there was actually an industry for it. Once exposed to a fire, the balls become bricks. I tried these, but I think they are too light. So I have gone to cement. Almost as heavy as rocks, and I can make about 30 per hour, and they are reusable. I have a big dirt hill I use as a backstop. I recover most of the cement balls.
Practice, practice, practice. I feel like a golfer at a driving range.