Some sinks and stove tops are stainless steel and some are aluminum. Aluminum is much softer, easier to polish but easier to scratch.
The grit you start with depends on how bad (deep) the scratches are. When you sand (polish) you are grinding away the surface of the metal to a depth equal to the depth of the scratches you want to remove. It is a process of replacing deeper scratches with scratches that are not as deep but covering a larger area. This process continues until the scratches are so minute as not to be discernible.
I've used this process for metal, fiberglass and automotive paint
. Works well but can be labor intensive and time consuming. Good luck.