I'm sure there is a "right" way to clean stainless steel, but I haven't found anything that works until yesterday! I was scrubbing my stove top with baking soda like I do every time I scrub it and I decided to just do the stainless part, on the back splash where the digital controls for the oven are, with baking soda too. I've always left this part to do separately because I knew you were supposed to clean it a special way. Everything I've ever tried to clean it hasn't worked, so I figured, why not? This is the part of my stove that gets all the oil splashes and then I can't get them off! A little baking soda paste and wah lah! All clean!
See how pretty it is!?! The front of my oven was really really bad, so when I was done there were still marks on the steel even though it was clean, so I used the magic wipes (they call them that, not me) and it seemed to help moisturize it. The wipes claim to clean, protect, polish and be fingerprint resistant. I've only found them to polish, but it was just what I needed.