Anyone using stainless cookware should be using Bar Keepers Friend, it's like magic on stainless steel.

The oxalic acid in it removes calcium buildup and helps passivate the stainless steel, the surfactant in it somehow dissolves browned oil stains (even the nasty burned in ones on the bottom of the pot) and the feldspar dust in it provides a bit of abrasive action. Smells funny though. And wear gloves.

The only extra work is it really needs to thoroughly rinsed off or the feldspar dust leaves white residue when it dries.

But seriously it makes stainless look like new.