For brightwork I use four different products.  All four work, but some better than others depending on what you're doing.
The first -- ammonia.  This is a good cleaner, most effective on small 
parts that can be removed and cleaned individually.  Remember I work mainly with radios, and this is good for bezels, pushbuttons, and knobs.  As an aside, plastic knobs and 
parts can be cleaned with Bleche-Wite.  Either one, spray on, clean with a paintbrush, wash off.  Just one caveat -- Studebaker.  Don't use harsh chemicals on those ivory 
parts used in Studebaker dashes.  Use Windex or a mild soap, washing frequently.
Okay, second:  Wheel cleaner.  Spray container, look for the type that says danger -- corrosive.  This has a mild acid which can indeed corrode some metals, but your stainless and chrome clean up great.  
Wire wheels -- perfect solution.  Again, my main use is on radio 
parts; this cleans ground-in dirt better than ammonia.
Third: Nevr-Dull.  This is a tin can full of cotton-like wadding.  Pill off a little and rub it in -- watch that chrome come clean.  This stuff is addictive -- start using it and you won't want to stop.  It DOES leave a residue, so be ready with a clean shop towel to eipe it off and polish things up.
 Fourth and not least:  Simichrome polish.  looks like a tube of toothpaste, and you can find it readily in any motorcycle shop.  A little dab'll do ya -- put some on a shop towel and go to town -- it cleans and polishes chrome and stainless and brings out a real luster.  I might add that Simichrome doesn't hold a monopoly on this stuff.  I've tried other brands that work just as well.  Simichrome is pink; other brands may be white.  Hmm . . . I wonder if it CAN be used for toothpaste?
I've also found Simichrome to work on polishing plastic 
parts.  I also have Novus Plastic Polish.  Simichrome works as a "rough" polish; seems to do a better job than Novus.  But I follow it up with Novus FINE.  Those 
parts will shine like glass!
Hope these give you ideas.