you need to get the special glass one if you really want your stainless steel to be shiny. It is smooth rather than towelling looking. Clean with damp cloth a and polish with cloth b. It really works and you don't need any chemicals.
The ordinary one is brilliant for general cleaning. I got a pack of five from Waitrose but it didn't polish as well as I expected until I got the glass cloth. I am nesting at the moment so I am obsessed with all cleaning products. You should hear me going on about my new mop.