The case should never be shiny, it was made to be a lttle like
semi-gloss. Some of the early ones were almost a flat finish.
When I had my shop, I always used Fantastic spray cleaner on the
cases. I have since used Orange Clean or Castrol's Super Clean if it's
dirty enough. Always, always take the case off the computer, take out
anything like the keyboard, switches, etc, and spray it down and give
it a good scrubbing. Rinse off with hot water, and blow it dry with
air if you got it.
For the brush, I like to use a 1-2" wide paint brush and cut off all
the bristles except for the last 1/4 to 3/4" and it makes a fine, stiff
brush, that gets into the little crevices and craters like a //e case,
but is soft enough bristles to do no damage. Experiment with the
bristle length. Has to be firm to really get into the small craters.