The best way to clean a suit is brushing with a Kent double-sided brush. Dry cleaning is overrated and overkill and should only be used for spot-cleaning stains. Make sure if you have a stain that the dry cleaner only spot cleans and does not press afterwards unless it is hand-pressed, which I understand is rare. Here in Japan, I have my suits hand-pressed. Even if you have a stain, don't panic at first Try dabbing it with a little water and gently brushing with the nap or pile if a light stain, with and against the nap/pile if deeper. Be sensitive to how delicate the cloth is. Steaming will not remove dirt from suits. That is for regularly brushing after wear. However, steaming will kill bacteria upon contact. But for shirts, the best info for that is here: http://www.customshirt1.com/ASK/laund01.html
I think I am lucky with my cleaner here in Japan: no starch, no bleach, no softener, and my shirts are hand-pressed.