First quantization is appropriate for studying a single quantum-mechanical system (not to be confused with a single particle system, since a single quantum wave function describes the state of a single quantum system, which may have arbitrarily many complicated constituent parts, and whose evolution is given by just one uncoupled Schrödinger equation) being controlled by laboratory apparatuses that are governed by classical mechanics, for example an old fashion voltmeter (one devoid of modern semiconductor devices, which rely on quantum theory—however though this is sufficient, it is not necessary), a simple thermometer, a magnetic field generator, and so on.
Initial quantization is the most suitable method for examining a single quantum-mechanical system (distinct from a single particle system, as a single quantum wave function defines the state of a single quantum system, which may comprise numerous intricate constituent components, and whose development is governed by just one isolated Schrödinger equation) controlled by laboratory equipment that operate within the realm of classical physics, such as an outdated voltmeter (although sufficient, it is not necessary), a simple thermometer, a magnetic field generator, etc.