OK - this is a complex one. Basically, propeller design varies by aircraft because you are trying to balance a bunch of conflicting design limits and factors. For example - you get more thrust from longer blades (larger swept area), but you have have to take into account ground clearance, and a limit on the prop tip speed which cannot exceed the speed of sound. While you get more thrust from more blades, the air vortex created by each blade can interfere with the next blade, so that sets an upper limit as to how many blades you can have (and yes, there have been 5 and 6-bladed props, and counter-rotating ones as well, but we are talking WW2 era aircraft here.
Now, also realize that the weight and drag of the prop (which is a factor of how many blades, blade length, width, and pitch) has to be balanced against the power of your engine. Aces High notwithstanding, most of the time the engine would be running at a cruise power setting to save fuel - engines have a particular power and rpm setting at which they are going to be most efficient, so what you are looking to do is get as much thrust from your prop as you can at that power and rpm. Balance that against the altitude you are likely to be operating (higher up means thinner air, which means you want bigger, wider props so you can get more thrust up there), and the performance you need while in combat at military / emergency power and it all becomes quite an interesting engineering problem.
Give a big <S>! to the aeronautical engineers of the day folks. They figured this all out with paper, pencil and a slide rule...