Aluminum for me is always the buff and polish... for what little I do of it cause I kept the patina on my bike.
Chrome, if really nasty, start with some glass cleaner or other lubricant and an SOS pad. The finer rust and grime, the nighthawker's solution (from nighthawk forum) has been aluminum foil and wd40.
For cleaning engines, I have one trick I use, and only that trick. Some will use oils, etc to hide the dirt, but to really scrub clean is is soaking with soaps and water, and I use those foam paint brushes (2" wide one) with the wood handle. Super cheap, and they have a firm center perfect for cleaning between fins.
The rest, 1" foam brush is awesome for scrubbing wriggly parts like calipers, nooks in frames, etc and tight spots on the wheels.
If the bike is really bad for dirt, don't try to scrub it all off at once. You can start scrubbing away paint, etc. Better to just do it lightly each time you wash the bike, and it will take off the heavyset stuff over time. Toilet bowl brushes are great for scrubbing tires! Especially if you have white lettering/whitewalls.