For a good cleaning, I'd say soak all parts in warm soapy water, then spray WD-40 through it, then run cleaning rods and patches through it, then soak in water again, run patches through to dry completely, and oil any moving parts.
Some may disagree on the WD-40, but I find it to work very well when it comes to removing build up. and have never had any problems with it.
If the barrel is severe pitting, I'm not sure what to do. But, I'm sure someone around here will have a good answer.
By the way, Welcome to G&G