Unless you are cutting thru the stainless or polishing paint, the tools you have there may not give you the finish you desire.
Generally polishing is done with an electronic variable speed 7" angle grinder and varying grades of polish. The buffing pads come in different weights as well. Generally speaking the lighter the colour the finer the polishing both in compound and in the pad/wheel. There are some compounds specifically for stainless steel but don't know exactly the name for them but the colour matches close to other polish of similar grits that are used on aluminium.
The grinder used is variable because you are quite capable of "burning" the metal due to the friction some compounds can generate. You usually use the slowest speed setting.
The compound to use would depend on where you are starting from and how polished you want to end up with. It is done in stages with a progressively lighter compound and buffing wheel.
The buffing pad comes in various designs with some ruffled material crimped in a centre hub. Some are layers of material sewn together to make a wider buffing wheel.
The smoother the compound + the smoother the buffing wheel = the better the reflection.
Here is a Canadian suppliers line up: http://www.truckerssupply.com/Polishing.pdf
Here is a chart of compounds: http://www.pjtool.com/jewelers-rouge-chart.aspx
Here is a link to get your wife to polish: http://www.amazon.ca/How-Win-Friends-Influence-People/dp/0671027034
If you just want to do a few touch ups on the rust coated spots try using some silver polish available at any department store.