Slingshots were fun when I was a younger kid. Dad made my first before I made all my own the old school way... fork from a tree, strips of tire inner tube, patch of leather, sinew. Had store bought when I was much older, typical Whamo and later a wrist rocket. But while still a young lad with my grandfather's help I switched to slings. Now that is a hunting tool, both for vermin control and for cook pot fodder. Even though I got my first firearms when still very young, I continued to use the slings into my high school years just for the fun and challenge of them.
My son went through about the same process. He started with an old school slingshot while Dad used a sling. Eventually he wanted to step up to slings, so we made his first together. Was a lot of fun for us to hunt with them, use them to while away some time on camping trips, etc. We could spend hours on a lake shore skipping rocks and throwing them to far corners of the lake, or knocking pine cones off trees, etc. While my son had guns from a very early age too, he learned how to stalk like an expert because of his slings.
They have more of a learning curve than a slingshot, but with practice you can get very deadly with them. And to far longer ranges than with a slingshot, and take much larger game with them. Good techniques need to be learned, pretty much underarm for distance, side arm and more over the top for shear power to match situations. Easy enough for us to learn control... I pitched youth baseball from PeeWee to Little Leagues and in high school, fast pitch softball in city leagues to mid life after college. My son baseball up through Minor League.
Most likely you already have all the fixings for a sling in your home/garage. My first ones were simply made from old leather boot laces, a piece of heavy leather cut from an old boot, and sinew. Later used 550 paracord and store bought materials, but nothing at all wrong with just the basic slings. Had different sized and shaped pouches with different size/type "ammo" cuts/holes for different ammo and uses for hunting, target and chucking rocks of various sizes, and cherry bombs, M80's, etc. From back in the early days I had tons of ball bearings from quite small to as big as a golfballs from aircraft (my Dad had a Seabee buddy who worked at an Air Force base after the war). As a regional marbles champion X times starting from 4th grade I had endless marbles for my hunting/target slings as well and for the endless marble cannons. A couple of sizes for rocks and I was set for any use. Was a David in a Goliath world for quite some time. To this day my "survival kit" still has a "rock" sling in it.
Low cost, lots of fun, and can be very useful. Found the below link you might check out for a starting place. But don't be afraid to experiment with materials and styles to find what works best for you and your style. Just make sure there in not much stretch (looses accuracy) and you'll be good to go.
http://slinging.org/index.php?page=how-to-build-and-use-a-traditional-apache-sling---l-w-forsyth
