Your question hasn't an easy fast answer. A serious propeller design from scratch is a thing that can only be performed by hydrodynamics labs.
The Goal is arriving to a propeller that at the desired speed, requires the minimum torque.
Propeller expulsion current at the desired vehicle speed, must be almost the same than the relative free flow speed. At the same time, fluid at the wake astern of the propeller must have the less possible induced rotation.
This way, the correct thrust with minimum energy consumption is achieved.
The general procedure is:
1-] Calculate total vehicle resistance at the desired service speed.
2-] Set maximum propeller diameter. Take into account clearence and induced wake field.
3-] Better propeller will have:
Best performance is achieved with maximum thrust provided by the minimum torque. Hence .....
Maximum diameter and propeller surface area ratio, with the minimum pitch and RPM would be the best.
Performance decreases with the blades number, hence the less blades the better, but, balance-vibrations and cavitation risk increases.
A balance between vibrations, cavitation, area ratio, pitch, diamater and RPM must be found.
Hydrodynamic pitch and thrust can be improved, at the same time than cavitation is held under control and torque is reduced, by means of selecting a correct blade profile.
But, fluid speed and resultant flow angle change along the blade, and hence the profile and the geometrical pitch must also change.
Behind each blade, a modified pressure-speed field develops due to the distortion created by the blade. Hence, next blade will not work on a "clean" field, but into a modified one.
Fluid adquires three main induced speeds; Radial, axial, and tangential, that change the hydrodynamic angles, speeds and the way they are distributed through the propeller.
At the tips, where the fluid moves faster, and the fluid hydrodynamic angle is minimum, high turbulence areas develop. The plan shape of the propeller (not ducted), must try to approach an ellipse in order to minimize this effect.
In short words:
The propeller is designed in order to work inside a fluid that has been disturbed by the propeller itself plus the hull.
Not an easy thing .........
Best way to go, is starting from the systematic propeller series, making the choice among them, and applying some modifications in order to addapt the standard to your vehicle.
The series to choose will depend on the navigation features of your design.