That setup from Harbor Freight will work just fine, airbrush and all. You don't need a tank, none of the airbrush compressors have a tank, they run non-stop. If you get one with auto shut off, the compressor shuts off when you let off the air brush trigger.
If you have a home compressor with a tank, of course that will work too. You need the regulator and moisture trap. I've used everything from a can of Propel, to a tire, an expensive compressor, home compressor etc etc. Doesn't really make a difference, you just need the regulator and moisture trap.
I've used about a dozen different airbrushes as well. Currently using the dual action from Harbor Freight for most projects, and a Master for detail work. There's a ton of stuff on this site and good prices....check it out:
http://www.tcpglobal.com/airbrushdepot/
Amazon carries stuff from them also if you're a Prime Member free 2 day shipping
