http://www.dickblick.com/zz250/02/ I have used a Badger 150 airbrush in the past but it was not for bow finish work.
The Badger 150 cost $100 and is a double action brush, which means that you can press the trigger and start the air before releasing any of the pigment or clear finish that you will be using. This is a good durable airbrush that is easy to get parts for. This brush has the capability of using 3 different size tips a fine, medium and large diameter tip.
The filter that you are asking about is a water trap. Its purpose is to capture the water that is in the airline. Without it, at some point, the airbrush will spit water out of the tip.
http://www.dickblick.com/zz269/66/ You will also want to look into getting an oil less compressor. A compressor with an air reservoir tank is the best because it will eliminate the pulsating effect that a diaphragm compressor will produce.
Hope this helps.
Tom