You can clean anything stainless with a good quality glass cleaner. Just spray your cleaning rag, clean and buff with another clean rag;
On stainless fridges, after cleaning, you can spray a rag with WD-40 a lightly wipe the fridge to retard future finger prints and smudges. DO NOT USE on stove or sinks as WD-40 is flammable and will contaminate food. I've used this trick on fridges on my flips and home....works like a charm
I only have 1 stainless pot ( the bulk are cast iron and just get a hot water rinse / scrub) and for it regular dish soap and a GOOD rinse. For the front of my stainless appliance a bit of window cleaner.
You need to keep in mind that the smudges are either cleaning residue...that is not properly rinsed away...or oily soiling that is not first cleaned away. As always identify the soiling type first then used the proper amount of cleaner / rinse.
example... basic water stains can be cleaned with more water while bacon grease will need some type of soap or detergent.
or those wonderful finger prints from kids and others!
I keep my ss appliances shiny & smudge free by using Simple Green. Mix some with water in a spray bottle. spray on the appliance or on a clean dishcloth. Wipe the entire surface then dry with a clean fuzz free dish towel. If there are still a few (this doesn't happen often) stubborn smudgges left, spray on full strength, wipe & dry. Keeping a spray bottle of Simple Green handy lets me wipe up more frequently which keeps the difficult stuff to a minimum.
believe it or not pledge works.
Make sure that the cleaner contains no chlorine. Chlorine is a natural enemy to stainless steel and came damage the surface easily. A better ingredient choice is ammonia. Water with mineral deposits (hard water) can cause staining and water spots to form on stainless steel. Always remember to dry your stainless steel surfaces with a towel after rinsing. When these areas form, people usually suspect the cleaner, but it may, in fact, be water that is the culprit.
Janitorial supply companies carry products designed specifically for cleaning stainless steel items. I used to use it all the time on my sink, pots and pans, etc. I never had to worry about smudges or anything like that. Just had to make sure that everything got totally dried after use.
" Bar Keepers Friend" in powder or paste is the best cleaner for everything in the kitchen and bath. It is safe to use...not bleach!!. You can buy it almost everywhere , walmart , Target, Hardware store for under $2,-
I use Barkeepers Friend as well. When I find water spots on the stainless steel I use a bit of WD40 and buff it out. A little bit goes a long way.
I use a wet sponge and baking soda (good way to use up outdated box) to clean, rinse then dry. then go over the area with mineral oil. It prevents/delays water marks from forming. Good luck!