I've recently found myself running up against all sorts of adjectives that can describe a model category: cofibrantly generated, combinatorial, tractable, stable, locally (finitely) presentable, (left and/or right) proper, simplicial, admits Bousfield localizations, et al. I'm hoping for a reference whose explicit goal is to give an intuitive explanation of these concepts; presumably, such a reference would also tell me what each of these adjectives can buy me.
(As a bonus, this reference might even have a diagram analogous to the one on pp. 576-7 of Gortz & Wedhorn's book Algebraic Geometry, which summarizes the relationships between different properties that a morphism of schemes may satisfy. But that'd just be for fun.)