Its more efficient to move a large volume of air at alower velocity than a smaller volume at a higher velocity to produce the same thrust.
For un-shrouded rotors, the optimum tip relative Mach number is around 0.8.
So if you select the maximum diameter that can be packaged, gear to the RPM that will give you a good tip mach number, then the power available will dictate the approximate solidity that you require to absorb the power at that RPM. The choice then between chord length and number of blades will depend on the efficiency, weight, cost, noise, availability etc of the possible combinations.
No simple answer I'm afraid, and the demands of ceiling fans are rather different from those of aircraft powerplants.