Airbrush - I recommend an Iwata Eclipse as a durable and reliable airbrush.
hose - to connect the airbrush to the air compressor.
Air compressor - Any air compressor is fine, provided it can be attached to the airbrush with the correct components.
A place that allows noise - Air compressors range in quality and noise levels. If the air compressor is a noisy, a place that can help absorb and muffle the noise would be best as to not distract those in the home.
vinyl/latex/nitrile disposable gloves - airbrushing can get messy, so having disposable gloves to prevent paint getting on hands is useful.
respirator mask - As these paints are being turned into a vapor, a respirator can protect the learner from the fumes and chemicals.
Acrylic Paints and Inks - Airbrushes require paints to paint. I do recommend inks as they are already thinned making airbrushing easier.
Airbrush cleaner - to clean the airbrush after the lesson.
Acrylic primer or Rattlecan primer - Acrylic primer can be airbrushed on to a miniature, or a spray/rattle can to prime the miniatures.
Cardboard/plastic liner/covering - to cover the table and protect the area from the airbrush spray.

Optional:
Airbrush booth - Airbrush booths have lighting and a fan to help ventilate the vapored chemicals.
airbrush varnish - to seal the miniatures.
 

As this is a miniature painting class, some miniatures may contain fantasy violence.