I shy away from soap on coffee gear, as it doesn't rinse as clean, and any soap left behind with break down coffee oils. Since espresso is partially an oil/water emulsion, anything that can break down oils makes for worse espresso. Cafiza, et al, rinse off much more completely.

As others have said, one of the commercial cleaners (I happen to favor Joe Glo because it foams less and is therefore more versatile, but it's a matter of taste) is going to be most effective. In addition to something like TSP, they also usually contain a fairly high proportion of enzymes. Most of them are essentially pumped-up versions of automatic dishwasher powder, more or less.

For daily cleaning, I tended to put a half-teaspoon or so of baking soda into a blind filter and do a quick rinse. It rinses cleanly and keeps rancid oils from building up between the weekly cleanings.

Best,
David