You should also consider the speed and stamina.
Yes, cavs are your biggest threat, but if you eliminate them early on (baiting one unit of slinger), then the rest of your slingers can pull and damage an entire unit of slower infantry.
Cost/Efficiency, i believe them to be more than decent.
I can't recall how effective slingers are against horses though. They have a superior range (on paper), but do they still do a lot of damage at that range ? Low-damage range units are often only used to kill horses, and demoralize/slowly kill ennemy infantry.
I still prefer archers (Cretan Archers !), but since you don't have that many armies around, guess you'll prioritize infantry. 2 archer, 6 infantry, 1 general, 2 cav, 1 siege, for example.