Thanks for explaining the background, it helps to know there's an experienced pilot involved.

In simple terms...

A larger prop of the same pitch can move more air, if it's spinning at the same speed. However, since moving more air requires more power, the larger prop will turn slower.

A prop of the same diameter, but larger pitch will move air faster, if it's spinning at the same speed, however, this will also require more power, so it will turn slower.

A smaller pitch, but same diameter, will require less power, so it will turn faster. Same goes for a smaller diameter, but same pitch.

A smaller prop with a larger diameter, for example 10x7, may end up using about the same power as something like an 11x6. In this case if you wanted a faster plane you'd go with the 10x7, but if you wanted better pull during takeoff, you'd go with the 11x6.

The "art" is in finding prop sizes that allow your engine to turn in the range that produces the best power. If your engine develops peak power between 12 and 13 thousand RPMs, look for props that let it run in that range. Going back to the example, perhaps the 10x7 and 11x6 are in that range. If you try an 11x7 and discover the engine only turns 10.5k, you probably wouldn't want to use it. Usually, the engine manufacturer has done some of this discovery for you and lists the props that work well for the engine.

Once you know what props work best, you can then choose the right one for your application. In general, the smaller pitches, perhaps with a larger diameter, will be like being in a lower gear in a car. You'll have more pull, but less top end speed. A prop with a larger pitch, but perhaps smaller diameter, will give you less pull, similar to being in a higher gear in a car. This means it can take a bit longer to accelerate, but you'll have a higher top end speed.