After about an hour of degreasing and scraping old, stuck on oil, I painted it with Annie Sloan Decorative Chalk Paint in Emperor's Silk. This red really is the perfect red and usually only takes one coat!
I built a little stand or shelf for the cabinet,
and painted the first aid white cross on it and finished with a glossy coat of urethane.
I see it as a fun "First Aid emergency medicine cabinet", i.e. liquor cabinet.
But, it would work equally as well in a bathroom as a real medicine cabinet.