Spray the cleaning solution (vinegar + water) directly on the fridge. Be generous with it.
Look closely, and you’ll see that your stainless steel appliances have a distinct grain direction - it will be going either vertically or horizontally. (All of my Samsung and GE appliances have horizontal grain.) Take a soft cloth or a microfiber cloth and wipe your appliances with it going with the grain. You'll notice that while some marks will wipe off, others won't. And that's okay for now!
Once your appliance is good and dry, put a little olive oil onto a dry cloth and rub it in - again, going with the grain. This is the step that will really buff out those unappealing fingerprint marks all over your appliances (and also prevent them from showing up.)