The idea that there are "adjective types and order" is a bit misleading; the underlying order is primarily semantic/pragmatic. The order is, roughly, extrinsic to intrinsic, situational to innate, contrastive to contextual; how closely attached a descriptor is to the head noun generally implies how "essential" a property it describes. This isn't really an English thing, either—English just happens to be the language most frequently taught to non-native speakers—but adjective order actually correlates pretty well across languages.

The oft-repeated opinion-to-purpose order of adjectives has decent descriptive power, but is easily oversold; the classes described do not have consistent ordering across contexts. The same woman may be an "old American woman" when interviewed for his opinions on global politics, or an "American old woman" in the context of comparing healthcare for the elderly across countries.

The "big bad wolf" is a fairy-tale villain; a "bad big wolf" is a failure at being a big wolf.