Air resistance complicates things a lot, but we can use calculations with no air resistance to set limits (no spin effects either- though I suspect these would be comparatively small).
The maximum range of a projectile on flat ground with no air resistance is given by:
R=(v^2)/g
R: range in meters
v: Launch velocity (magnitude of)
g: Gravitational constant 9.81 m/s^2
By using this formula you can set theoretical maximum range per initial throw velocity, or a theoretical minimum throw velocity (and therefore muzzle energy if projectile mass is known) for a given range.
Launch speed - maximum possible range
10m/s - 10m
20m/s - 41m
30m/s - 92m
40m/s - 163m
50m/s - 255m
60m/s - 367m
70m/s - 499m
80m/s - 652m
90m/s - 826m
100m/s- 1019m
Range - Theoretical minimum speed
50m - 22m/s
100m - 31m/s
150m - 38m/s
200m - 44m/s
250m - 50m/s
300m - 54m/s
350m - 59m/s
400m - 63m/s
500m - 70m/s
600m - 77m/s
700m - 83m/s
800m - 89m/s
900m - 94m/s
1km - 99m/s
The ranges and speeds above are essentially the 'correct' answers if air resistance (and spin effects) were none-existent.
For example it is physically impossible to throw 200m if you cannot impart an initial speed of 44m/s- and if say, your absolute highest launch speed was 50m/s then it would be physically impossible to throw further than 255m.
There is some evidence (the slinging paper) that these numbers could be relatively accurate if you are using ammunition such that air resistance is very small and has little effect (lead glandes etc). On page 79 a computational method shows lead glandes achieving 170m vs a theoretical maximum range of 187m (one could imagine tungsten glandes falling somewhere in between).
Here less aerodynamic projectiles are significantly impacted- the clay balls achieved only 105m from the same projected initial velocity, I imagine that natural stones are at best similar to this and at worst, much less- requiring far higher launch speeds than the calculated minimum (though the calculation of so is only possible with computational methods).
Also interesting is that the positive effect of using a biconical vs a ball is stronger in clay than lead- as any further improvements bring it ever closer to the theoretical maximum range.
Slinging paper:
http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1032&context=anthrothe...