You need an adapter that Badger makes. It is on this page:
http://www.badgerairbrush.com/access2.htm
and is part no. 50-023. It adapts the 1/8" threads on your airbrush hose to standard 1/4 NPT threads that will fit your compressor. Alternatively you can get an air hose that has 1/8" threads on one end and 1/4" NPT threads on the other. Badger makes them to.
The compressor you have will work fine. It is basically what I use as well. If it becomes to onoisy, just let the tank fill and turn the motor off. You can paint from the air in the tank until it get low. I can go about 30 - 45 minutes with mine.