There are two essentials for stainless cookware -- Bar Keeper's Friend and vinegar.
Bar Keeper's Friend will remove the dark stains and those bits of food that don't quite come off after you heat up water in your pan. It serves the function of a cleanser without incorporating the grittiness that can mar the finish of your stainless.
So, what's the vinegar for? Salt or other factors can create a chemical reaction with the stainless that may generate colors that bear a remarkable resemblance to the colors of an oil streak -- blue and pink stains that cannot be scrubbed off. But, put some vinegar into some water and, voila, those oil-streak colors vanish!
Between the two, you can keep your stainless looking factory fresh for years. You don't need to use both each time out -- possibly neither. The nature of what you're trying to eliminate from your pans will tell you which to use.