Why are there so many different propeller shapes?
The best design depends on what your goal is. This changes with operating conditions:

Best power/thrust ratio

For lightly loaded propellers this would be minimum induced loss. These are the propellers on human-powered aircraft, windmills or motor gliders. Minimum induced loss is achieved by distributing circulation elliptically across the propeller disc, and a typical consequence is a small chord near the tips and a low number of propeller blades. If you want to research this more, I recommend to play around with XRotor by Mark Drela (and maybe reading this). Mark used it to design the MLE (below, NASA photo EC87-0014-8) and Dedalus propeller.



Maximum thrust at high speed

Highly loaded propellers, which can be found on large turboprop aircraft, are less concerned with induced loss, but need to put out as much thrust as possible with a limited prop area. The diameter is restricted to limit tip speeds, and the tips typically are mildly supersonic. To limit the suction peaks on the blades, the local lift coefficient needs to be low, which is achieved by increasing chord and the number of blades. Increasingly, now tip sweep is also used, but this drives up the torsional loads on the blades and leads to warpage in operation. An extreme example is the P-27 prop on the D-27 turboshaft of the An-70 transport (below, picture by Marina Lystseva).



Ship propellers

They operate in a medium which is 800 times denser than air, and the main concern is to avoid cavitation. This again means to limit suction peaks and leads to very high blade chords. To limit draft, ship propellers need to have extremely small diameters.



Submarine propellers

For submarines, add  minimum noise emission to the design goals. Minimum draft is not a concern, so the propeller blades are less stubby. Their sweep distributes the cutting through the wake of the rudders over time, which helps a lot to reduce noise.



The fancy shapes of some model aircraft propellers have more to do with marketing or unscientific voodoo beliefs by some hobbyists. Generally, a straight shape works best.