How to use correctly a microstepping driver with a lower voltage stepper motor I want to use a microstepping driver like Haitronic's HS2215 with a NEMA 17 stepper motor with rated voltage of 4.2V and rated current 1.5A.
The input voltage range of the microstepping driver is 9-40VDC.
From what I understand,  I can use the switches to set the maximum current. In this particular case I would use SW4=On, SW5=On, SW6=Off.

TB6600 current settings
You can adjust the current that goes to the motor when it is running by setting the dip switches S4, S5, and S6 on or off.

I've found this Maker's Guide which describes the settings for use with an arduino.
However, I am not certain what voltage (VCC) should I supply to the mircrostepping driver? Should I provide, the minimum of 9VDC, should I provide less? Is this irrelevant?
That doesn't matter at all.
The voltage stepper motors are rated for is the voltage that, if applied to the motor coils, would create its rated current.
Stepper motor drivers monitor the current, and always use the full voltage available to them (9 - 40V in your case) to drive the stepper motor - using PWM.
The stepper motors coils inductance slows down the change in current, allowing the driver to reach its set current.
Higher drive voltages simply mean that it's easier to overcome that inductance, allowing for faster stepper motor movements.
You'll want to set your driver at 1.0 or 1.5 A, and supply it with as much voltage (up to the rated 40 V) as you can.