accuracy is the most important one.

Does not matter how hard you can sling if you can't hit what you aim at

super strength or speed = power if combined
because then you would be like hulk+intelligence you already have and you don't neccessarily need to sling, you can throw boulders and by hand it's gonna be easier to aim. the accuracy can be worked.

if the trait is in the sling then high accuracy would be boring, no challenge... but high power with average accuracy would be a disaster .
maybe have a set of super slings in his pocket: high power , high accuracy, infinite ammo etc

the hero slinger i have in my mind is a hardcore guy covered in dirt wearing his tunic in all climates, never complaining doing the dirty jobs, clearing passages for the army, highly skilled but doesn't care

he also needs a beard

If I have super strength, why would I need a sling?  I can just pull up a tree and throw it at something.   

Super speed?  I wouldn't need to throw anything, I could just run up and hit it with a rock while going super fast.

If you don't hit them, you won't hurt them.

Infinite self reloading pouch?  Still, if you don't hit them...

I have no idea what that is.

You know Morphy, you come up with the coolest answers...

Morphy, I was hoping someone will say that =D

And yes, you can throw a truck or tree with super strength, and so on - but that's beside the point. But slinging 1m diameter rocks - you are, in that case, a catapult

Maybe I made a mistake not calling ability "super accuracy" - like 100%-hit-him-in-the-eyepupil-through-visor kinda accuracy

Bill, Green Lantern Ring is "ring that grants the wearer incredible and incomprehensible powers and abilities by harnessing willpower". So, basicly - sling you can change with your mind, from short sling to long sling to staffsling or any other, depending on what you need at the moment.

Sarosh, I imagine you hero like combination of Mad Max and Clint Eastwood from spaghetti westerns. Looks promising =)

This might ignite another flame war, but I just love that accuracy is a “superpower” when it comes to slinging. It’s certainly not something that comes easily for us mortals. 

If I had the infinite ammo pouch, I’d also want an “infinite mortar trowel” to build some sweet rock walls out of all those free river rocks... unless the infinite ammo is made of lead. If it’s infinite lead ammo, then I wouldn’t want to be responsible for the hazmat cleanup.

Here you go - now it's super accuracy 
Like I said - 100%-hit-him-in-the-eyepupil-through-visor accuracy