Most of the Craftsman compressors have 1/4" NPT fittings on them. An airbrush will usually have 1/4" NPT or 1/8" NPT fittings. Take your airbrush hose with you to Sears and see if it screws onto the fitting. If it does you are good to go, if not you'll need an adapter.
All of the Craftsman compressors I've seen do have a regulator on them, but I don't pretend to have seen them all. About the only compressors I know of that don't are the low-pressure airbrush only compressors.
Also add a roll of Teflon tape to your list. Wrap a layer around the threads of the fittings before you screw them together and they will be airtight. It's available in the plumbing section of any decent hardware store.