Scrub well with an SOS soap filled pad...

If perchance the surface is what they call "brushed", after you have cleaned it you can take a fine emery used in auto refinishing and do some remarkable scratch removal.

Try Bar Keepers Friend. It is a mild (oxalic) acid and will clean stains and scratches off stainless steel. It will abrade the surface a little. Your sink won't look brand new again. But it will look clean and much more attractive.

This is what you are looking for and I have used it many times and it works like a charm. The sink will look new.
It is called SCRATCH AWAY Stainless Steel sink Restoration Kit. The kit contains these pads and you start with the coarsest grade of crystal pad to the finest. The directions are easy to read and the results are amazing. I bought these at Home Depot but I am sure you will find them in the other big box home improvement stores

Don't use steel wool or SOS pads on you SS sink (old or new). It will add scratches that may soon start to rust. I use Barkeepers Friend on my sink when there are stains, but it's relatively new and isn't damaged. Most of the time I maintain my sink by just washing it with dish soap. That Scratch Away Kit sounds like the thing to restore your sink. Good Luck!

Probably you have cleaned the sink by now BUT.. I worked in Plumbing & AC office 10 yrs. Bar keep friend is the best for your sink. But you meantioned paint on it, I would use a little paint remover (turpentine perhaps) and then the barkeep friend.. however a master plumber who worked for me said to keep it shiney (not the new 'brushed" finish they have now) but a regular SS sink, is a lemon. Cut it in half and rub across the sink like it was a rag. Good Luck. P.S. Barkeep Friend is probably on the top shelf in the store because of its price. But well worth it.

I, too, have an old stainless steel sink and what I use is Soft Scrub with bleach. It seems to work wonders and I use it all the time!