I haven't had any trouble with rust following steel wool use on SS, no.
The best cleaner I've found for SS is Barkeepers Friend (I've done experiments, and interestingly found the powdered product to be LESS abrasive than the liquid version of Barkeeper's Friend). It does a good job of removing stains. I usually use it with a Scotchbrite pad, and am careful to use it with the 'grain' in the SS. (NOTE: I would NEVER use Barkeeper's Friend on an actual kettle-- it will put tons of micro-scratches on the surface.)
I've also removed scratches from SS by sanding them with wet-or-dry sandpaper lubricated with cheap 'SS cleaner' sprays. What you're actually doing is not removing the scratches, but disguising the scratches by putting fresh 'grain' on the SS. The point being that it's essential that you very carefully sand in a very straight line, and very consistently across the whole surface.