I'm surprised it doesn't already have a regulator on it. Virtually all of the Craftsman compressors have a regulator of some sort. Are you sure there isn't one already on it?
Other than that and the noise it will work just fine. I use a "General Purpose" Porter-Cable compressor.
As to other air sources, an air tank or compressed CO2 are probably the most popular. The cans of Propel (and other brands) don't work that well and get expensive pretty quickly.