Airbrushing Freehand is where most people begin. It can be frustrating and fun at the same time with the highly technical movements required. To paint with an airbrush, push the trigger down for air, pull it back for paint flow and forward to lessen paint flow, move the brush forwards and back to adjust line size, and up, down and sideways to draw - all at the same time. If you can pat your head and rub your stomach at the same time then switch, then you'll be airbrushing in no time. This does not however qualify you to drive and talk on a cell phone simultaneously.
Buy the best equipment you can afford, it really isn't but a few dollars more and holds resale value better if you care for it properly. Many students buy a hobby airbrush with cheap parts and a hobby compressor that doesn't pump enough air to make the paint flow smoothly. When they can't get a straight line or a smooth gradation, they think it's their fault and give up. Don't do that!
A dual action airbrush like the Paasche VL, Vega or Iwata HP series are good airbrushes that will carry you from beginner to pro for well under $100. You will also need a decent tank compressor that can pump at least 55psi. A good silent running compressor that will hold it's resale value can be had for around $300.-$500. If you can handle the noise, or run an airline into another room, any $50. tank type compressor will do from a discount tool store. Pick up an airbrush magazine at your local bookstore and get a subscription if your serious about learning. And buy every book out there for now and future reference!
These freehand illustrations were all done on inexpensive, smooth tooth or normal canvas with "Aqua Flow" or "Golden" acrylic paints. but any well mixed acrylic with the right viscosity or an airbrush formulated acrylic will work.