Beware, long post.

When searching for the "best" RPM there are no quick and ready solutions, because one has to consider a few things to get all elements of the system adjusted to each other.

First
Like already said, what is the power curve of the particular engine, and as important: what does the torque curve look like.
second
How does the muffler used, influence the power and torque curves.
Third
What plane is to be powered. Pylon >>>> Floater
Fourth
What prop tip speed are you after. Low noise (0.6 mach max.) or noisy (>0.7 mach)

For power, it is best to prop static between max torque, where the engine is at it's best efficiency, and max power, so the engine can unload in the air to achieve maximum power.
This power not necesseraly translates into plane performance, because propellor efficiency and plane drag factor also enter the game.
A high drag floater is better off at lower rpm near max torque. This allows a large, lower pitch prop with an equally large and relative slow propwash. This provides high efficiency despite the bulky fuselage.
A sleek narrow speed plane should use a small diameter high pitched thin bladed prop. The fuselage is not the limiting factor, so prop wash speed may be higher, and thus the end speed that can be achieved. RPM at top speed should be at peak power rpm. Tip airflow will be supersonic in many cases, so the planes are noisy by nature, even in the presence of excellent mufflers.
A 3D plane also has a narrow sleek fuselage to keep fuse drag low. Since no high speed is needed, and best prop acceleration is the goal, the prop load should be light enough to achieve peak power rpm at low speeds, in order to have best prop acceleration from reduced throttle rpm. At the same time, a high volume, low speed prop wash is required for best efficiency and control surface action, which relies on the propwash. 3d flight mostly is low and near, so sonic prop slap is a nuisance to be considered if you fly together with other pilots, or when the field has noise restrictions.

Even then, experimenting in search for best results is necessary.

Trends:
In Europe, the trend is towards lower rpm because of noise limitations, so a lot of work is being done to find a prop that allows the performance we are after at these reduced rpm, and yet achieve good 3D flight, which is becoming increasingly popular. Electric flight already took over in the small plane classes. The high torque outer rotating magnet motors are coming of age, so soon decent sized 3D planes will be electrified as well.