Step 2: load the sling with bullets (a piece of flint, iron ingot, or gold ingot)
 [>>-i>] ---> 1x (a sling loaded with the appropriate ammo type)
You now have a tool with a limited number of uses, like a flint and steel. Right clicking counts as a use of the tool and fires a bullet, with a delay between shots of maybe 1s to 1.5s, or at least 50% more than the delay for arrows if that ever gets increased. A loaded sling has 33 uses before running out of ammo and wearing out, regardless of what it is loaded with. Flint, iron, and gold bullets do damage like fist, wood sword, and stone sword, respectively. That's right, gold makes for the most powerful weapon here even though it's soft and creamy like lead, because density counts for more than hardness with bullets. Being hit with a sling bullet also causes a bit more knockback than other weapons.
Now that we have a way of assigning and crunching numbers, it's possible to compare slings with arrows, and make sure slings are weaker but still useful. Being realistic here, slings would consume otherwise useless gold, and do so more efficiently than arrows use iron. The best way to keep things balanced is probably making arrows use iron more efficiently, rather than making slings weaker. In any case, the fact that slings use cheaper materials than bows is adequately offset by their lower damage, lower rate of fire, consumption of string, and relatively low portability (since a stack of arrows holds 64 shots, while slings hold 33 shots and don't stack).