The transmission gear analogy doesn't seem to be getting through. I'll try the literal approach.

First, deal with pitch. As stated above, pitch moves your plane forward. The more pitch you have, the more forward you go with each turn. If you engine can turn 13k rpm, then raising the pitch increases your top speed.

However, more pitch means the engine must work harder. Therefore, we must lower the diameter of the prop in order to keep turning that 13k rpm. When we do that, we lose some pulling power because the prop is now not moving as much air per turn.

"But," you say, "I want more acceleration and the ability to go vertical better." So we go to a bigger diameter prop to move more air which helps it to hold its position when there is lots of drag or when the engine is having to do the work to fight gravity. So, again, we overload the engine by increasing diameter and so we must give up some pitch to keep our rpms up.

So prop selection is finding the sweet spot between acceleration and vertical performance vs. top speed. In flight, the bigger props really do act like low gear in a car because you get instant acceleration and instant deceleration, but can't go fast. And the smaller ones with more pitch are the opposite. To find the right one, start in the middle and then decide what, if anything you would like to change.