Beware, stainless steel is a lie, it can stain. I have a black spot on my sink and I have no idea how it was caused/got there, or what to do with it. Putting up with it for now, but I'd suggest not using anything too harsh.
I always find the best thing to do is fill the saucepan up with hot water and some washing up liquid. boil it up and leave it to simmer for about 30 minutes. empty it out and wipe it round or use a little brush to finish off. Has never failed. Brenda x