With my enormous Herculean muscles, naturally I experience no pain whatsoever....
Seriously though: Once after slinging repeatedly with friends, I experienced a great deal of pain in my shoulder. It took about a week for it to pass fully, but after it did, my shoulder felt stronger, more powerful, and I could sling for longer periods with no adverse effects. Occasionally I hurt my wrist if I use a big rock and don't control it well, but most often slinging is a painless experience. Except for whatever is on the other end.
The Perfect Rock, eh? I have plenty of rocks perfect for slinging; the absolute perfect size and shape. I live in the far south, so I am right near the coast; good stone (and sand) beaches nearby, with lovely rounded stones. Also, there is a large amount of woodland nearby, plenty of game, chalk cliffs for flint, an abundance of roots and greens, brilliant soil... in fact, everything you could hope for for survival purposes. The problem is that it is so amenable to life that people are nearly everywhere, agriculture has taken over, there are loads of towns... etc. *sigh* So that's progress...