Your line/string plays an important part too. Lighter line lets you throw farther, but it must be strong enough. If it dosent have a slick finish like poly?propeline or? it will not slide over a limb very well.
For throwing I would guess one to + lbs. Lead shot in a bag or?Baseball or hard rubber with a d-ring or screw eye for the line. Sooner or later your throw will come down on a roof, yard ornament or dog so something without sharp edges might be better. It is also possible to grab the line as it is running out to keep it from travelling past and into another tree, get the sun in your eyes, and get slammed in the gut as it swings back at you. Or so they say. Haha
A small bucket with a lid works great to keep it in. Flake/jam the line down in the bucket hand over hand without trying to coil it. Leave the weight tied on and put it in the bucket last after you put in a piece of cloth to keep it separated. The line comes out clean and will hardly ever tangle. If you do it from the ground it will get wrapped in sticks and...
Its too hard (for me) to throw it like a baseball. Tie a slipknot about 18" from the weight,pinch it there and underhand it after a few back and forth swings. Or with back to the tree, between your legs then over your head and it will really go.
I have seen guys that were unbelievable with a throw bag, but I am next to worthless so I bought a Big Shot and it does wonders. Its fun to play with and impresses little kids.