I'm going to decent here having just been introduced into the sling word by Doc Canada and his friends last weekend. First, having proper instruction on technique, like anything makes a world of difference. I had the benefit of Doc's buddy Louis give me some 15 minutes of instruction on stance, swing and throw which made all the difference in the world. Then Doc Canada provided me with one of his slings which has some nice design features about its pocket that make it very effective. Haven't had a misfire yet even while practicing with it with a bunch of folks.
As far as accuracy is concerned, I'm not there yet. But I am starting to get much better than I used to. Fifty feet is probably a good range limit. With a sling, you can throw way more farther than you could by hand. You can also throw much heavier rocks without injury to your arm. Where it is limited is that it won't work all that well in tree cover (like any projectile), but slings more so because you have to be clear enough to be able to throw effectively. Also, I agree with Doc Canada that you would be more effective using traps than slings.
Like Siguy said, getting into slings is a pile of fun. Whether you are throwing for distance or for accuracy. The guys I have been practicing with took to it very quickly, all of us were amazed at how little practice it takes to be able to throw something much faster, further and heavier than you could by hand. There is something about standing by a lake or a river in flinging our rocks that is almost endlessly entertaining. Its even more fun with a sling. I think I'm going to keep practicing with mine. In terms of equipment, a piece of string with a pocket is all you need. It weighs nothing, gives you a sense of nostalgia and is fun. What is not to like about it?
Size, shape and weight of the rock seem to make a big difference and as Doc's friend pointed out, everybody seems to settle on a throwing rock that has the right dimensions for them.