I briefly mentioned my choices. Let me explain them.
Martial Classes
Fighter - Base class of the game. Combatants defined by their traditional martial expertise. Experts in weapons, armor, tactics, combat leadership, marching, running, discipline and fortitude, carrying things, and generally everything that goes into an ideal warrior. Incidentally, a monk is just a fighter with a particular focus on say unarmed and unarmored combat and self-discipline - "martial artist" is a big clue there.
Fanatic - Combatants that channel their emotional energy (often fury) to transcend normal human limits. Why not barbarian? Because barbarian has too much unneeded baggage for a base class. A raging berserker from a primitive northern tribal society is just one type of fanatic. You can think of "barbarian" as a fanatic subclass if you will that has some extra wilderness knowledge. If you play DBM this is warbands as opposed to swordsman.
Explorer - The jack of all trades of martial classes. Martial skill monkeys with advantages in movement, navigation, survival, social interaction, use of beasts and vehicles, improvised weapons, and really anything they want to get good at. Mine are particularly good at using a weapon in each hand because they started out as a "sailor/mariner" class. Generic adventurer class.
Hunter - Assassins, slayers, hunters and killers that specialize in destroying particular foes. Experts in tracking, ranged combat, critical hits, and inflicting massive damage even against targets that are normally resistant to damage (such as undead, constructs, oozes) using knowledge of esoteric techniques and weapon preparation. Why not the Ranger? Well, because like Barbarian, ranger just carries too much baggage. Not every hunter is proficient in wilderness lore, good aligned, and dabbles in magic. That's a very specific build.
All martials are heavily customizable by mix and match feat selection. In fact, you can think of these all as good attack bonuses, good hit points, and lots of bonus feats. Multiclassing between them is pretty easy to get the blend of skills you want.
Skill Classes
Rogue - 3e IMO actually got the rogue pretty solid overall. You could make an argument it shouldn't exist, but I think that there is enough history behind it to justify it despite the objections to "sneak attack" as a combat schtick.
Paragon - The class for characters that aren't obviously skillful in anything but seem to always be lucky. Fortunate or blessed characters, prodigies and naturally gifted individuals. If in a story the character doesn't seem nearly as powerful as the other characters but is always saving the day anyway because things just work out for them, they are probably a paragon.
Expert - ??? I feel there is a missing class her of just generically knowledgeable. "Sherlock Holmes" is I think the archetype, but you could also make the case for Dr. Who and many others. The problem is despite lots of trying and lots of ideas, I can't make this class work in a D&D framework because it's hard to give them a schtick at combat that works at tier 3 or 4 and is unique to them. I feel like it would need to be "tricky stunts" but that's such a situational schtick that depends so much on the environment that it's hard to make it really reliable. Design in progress.
Full Spell Casters
Wizard - Non-spontaneous arcane caster representing all varieties of caster who master magic through study, mental discipline and self-mastery. Can be diversified by school of magic they specialize in.
Sorcerer - Spontaneous arcane caster representing all varieties of caster whose magical prowess is based on innate gifts or talents. Diversified by "Bloodline", these are the cursed, the gifted, the mutants, and the children of exotic births and parentage.
Cleric - Non-spontaneous divine caster representing servants of divine powers who grant their pious followers spells to further the divine's wishes in the moral realm. Polytheism and formalize religion. Diversified by the domains of the deities they serve.
Shaman - Spontaneous divine caster representing natural casters who receive their powers by bargaining with, intimidating, or binding spirits to their will using their esoteric knowledge of the spiritual world. Animism and informal religion. All witches, druids, warlocks, pact binders and the like are shamans or multi-classed shaman/arcane casters. Diversified by the totems they select which correspond functionally to the domain's clerics use.
Half Spell Casters
Champions - Exemplars of virtue, often selected by the gods to be their mortal representatives. Diversified by portfolio according to the gifts given to them. Why not Paladin? Because paladin is just one very narrow type of champion of a particular sort of deity with a particular sort of alignment and portfolio. That Paladin has been broken as a class has been known as long as the existence of "anti-Paladins".
Bards - Arcane caster jack of all trades. Personally, don't think I'd keep them and rarely see players play them, but they have so much history in the game at this point and enough of their own schtick that I don't feel I can leave them out.
That's 12 (13 if you count the unrealized Expert). That's plenty for core classes. Anything narrower than the above is probably either a build of the above, a multiclass combination of the above, or specific to a particular setting.