To clean smudge marks off stainless steel appliances, make a paste of baking soda and water. Rub over the spots. Then wipe the appliance down with plain water, and dry.
I own a 4-slice stainless steel (commercial/restaurant) toaster that I won on eBay about 4 years ago.
I did the same thing as you suggested and made a paste of baking soda and water. I also removed the crumb tray and unscrewed the bottom plate, and did a thorough cleaning. The baking soda and water did an excellent job in cleaning the stainless steel.
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