Bar Keepers Friend is good stuff. We use it for heavy cleaning, then rinse well and use a polish that leaves something behind to help seal the metal. Our favorite or I should Lena's is, Collinite No. 850 Metal Wax.
Liquid Metal Wax » Collinite
....I polish with Flitz, you can find it in almost and hardware store. Polishes SS great and leaves a very light protective coat behind. I have used it for 20+ years.