Here is a couple of restoration cleaning tips I've used recently. Obviously use at your own risk and test out on a small area first.
For removing hard sticker residue with traces of paper left I found that any abrasive type rubbing can mess the surrounding finish. Instead of using something like goo gone, I found that a small ball of paper towel soaked in warm water with a dab of kitchen dish washing detergent works. You apply it the same way you would use a poultice to a wound. It sticks in place and keeps the detergent on the spot while the warm water also helps soak the area. Use clear detergent if the finish is at risk of being stained by the dish washing detergent.
For removing soft stickers I found if the sticker area is warmed slightly and you remove the sticker very slowly then the residue will break away from the surface. You can also reapply the sticker and slowly lift it off again or use another sticker as extra adhesive pulling power.
For removing stainless rust and a mild oxide abrasive cleaner, wet ball of paper towel and dip it in a little baking soda (bicarbonate of soda). The baking soda is too abrasive for a mirror finish on some surfaces so afterwards use plastic, stainless or glass polish if requiring a high polish. Baking soda does leave a residue so will need to be cleaned off with a little water or whatever is compatible with your surface.