Choosing good projectiles will have a major impact on shot accuracy. All other things being equal the projectile can be the difference between hitting or missing your target. Safety is also an important consideration in projectile selection. Projectiles that are wet, muddy, slimy, or too angular can catch on or slip out of the pouch or throw erratically.
Two factors affect projectile quality: shape and weight.
Shape
To understand the best projectile shape for slinging it helps to understand that a sling imparts a spiral or spin on the projectile as it rolls out of the pouch upon release. The ancients understood this principle and found that a shape similar to the modern American football or an almond shape worked very well for slinging. Not only do these shapes take advantage of the spin and aerodynamics of slinging but they also seat nicely across the pouch making it easy to load.
However, you will rarely find perfect projectile shapes in the natural environment. So we work with what we have and do our best to avoid angular shapes. Stones with flat sides or sharp angles can catch in the pouch and throw erratically or curve dramatically, seriously affecting sling safety and accuracy. You will quickly grow accustomed to spotting good shapes ans sizes to throw with. Most slingers rarely pass up a chance to snatch a good stone whenever they see one, slinging or not.
Weight
Keeping your projectile weight relatively consistent will help slinging performance. Over time you will find that you gravitate toward a particular weight of projectile. That weight will probably fall in the rage of 50-115 grams. Strength, technique, and sling length will play a role in your decision and throwing somewhat consistent weight will improve performance.
Also, just as you instinctively know not to throw rocks that are too heavy, the same principle applies to slinging. Going too heavy is likely to cause strain or injury.
There is a notable projectile that nearly all serious slingers become proficient with; the humble tennis ball. Tennis balls are nearly universally accepted in the slinging world as the preferred practice projectile. Shape, weight (56g), availability, and relative safety will make the tennis ball your go-to practice projectile. Another benefit of tennis balls is that they will curve more easily than good stone projectiles and this will force you to learn spin control. Being forced to learn spin control will make you a more accurate slinger. More on spin control in the tips and trips section.
Modern slingers are often surprised to learn that ancient slingers did not always use heavy projectiles. Archaeological evidence indicates that light projectiles between 25-60 grams, were the most commonly manufactured (lead and clay) projectile size for ancient warfare. It is difficult to know what natural stones the ancients may have preferred to sling with but lighter manufactured projectiles were definitely popular.