The main point is to maximize the thrust that can be attained with the power available. Having a given power delivered by the engine at at given angular velocity, you should match that angular velocity to an optimum propeller. Thrust is obtained by accelerating a mass of air, and that's precisely the rôle of the propeller. Imagine you have a propeller that accelerates a mass of air X to a speed Y. In terms of energy, the cost of obtaining a given amount of thrust is halved if you double the mass of air and accelerate it to only half the speed. In other words, with a prop accelerating a mass of air 2X to a speed 0.5Y you get the same thrust for one-half of the energy delivered by the engine.
Hence, the bigger the prop, the better. Of course, you are limited by the tip speed, that has to be kept well subsonic, and by the speed to be attained by the aircraft, that should be relatively low. Helicopters use those large rotors for good reasons...
For an ultralight, slow and with little power available, you should use a propeller as big as possible, driven through a reduction gear in order to keep the tips below the speed of sound.