Going to brainstorm something away from my normal preferences, just for fun.
a) Assume 5e definitions for levels; level 1 is a novice with training, 10 is the hero who saves regions, 20 is planar challenging near demigods.
b) 3e-5e multiclassing rules.
c) Classes are strictly diegetic. Most people don't have classes, and those that have classes are recognizable as such in the fiction. The general capabilities of a class will be known within the game's main areas, and the population will usually have some opinion on the value (or lack thereof) of a class.
d) There are some strongly supernatural classes that open up at levels 6 or 11, that require meeting certain diegetic requirements (like paladin).
Classes
1) Not-a-class/Pseudoclass. What the people who don't get classes take. Each level here provides no Hit Die, but does give 1 feat, and counts as a level for level-based abilities and for proficiency progression. This is how you skilled level 5 farmers, who are still vulnerable to stirges and orc raiders. They're good at what they do, but they're not warriors except in desperate times.
2) Militia. Basic combat training, learning to defend and guard their town or country. The class of town guards and conscripted soldiers. A veteran Militia has defended against monsters and bandits, and understands the demands and horrors of war. Level caps at 10.
3) Ruffian. The guy on the wrong side of the tracks. Not a street urchin or pickpocket, these are the guys who the urchins turn in their ill-gotten gains for protection. Enforcers, bandits, underworld toughs, and vigilantes. Combat skills, stealth skills, and some street skills (or nature skills if they're raiders or bandits). Level cap at 10.
4) Bard. Everyone loves when a bard comes to town. Masters of performance, inspiration, and socializing. Although subtle at low levels, bardic song is true magic, and is capable of wonders as the bard learns ancient techniques and melodies.
5) Ranger. Bound to a nature spirit through ancient ritual, the ranger gains enhanced perception and a communion with nature. They are trained in both bow and blade, and learn a smattering of magics to become elite trackers and hunters.
6) Knight. A scion of nobility, trained in horsemanship and warfare. Skilled at fighting in heavy armor, and receives the deference due to his stations. Level caps at 10.
7) Chosen. Many swear the vows of the clergy to serve one of the many and varied gods. But the gods are fickle, and only a few so sworn are made Chosen, granted a portion of their god's mantle to do their works in the world. These blessed are considered greatly holy by their god's worshippers, and held in contempt by their god's enemies.
8) Healer. Beloved by the populace, these masters of holy (white) magic are commonly trained by orders sworn to gods of light and protection. Although not skilled combatants, they wield strong magics of healing, protection, and warding against the denizens of the shadow.
9) Druid. Ancient, fierce guardians of the seals that protect the world from the incursions of both gods and primordial beasts. Skilled in the magic of shaping wood and stone, calming and nurturing beasts, and calling wind and storms.
10) Shapeshifter. Among all races are those reviled few who are born with the changeling's gifts. As they master their talents, they can assume the guise of any man or woman born, and eventually turn their form into that of beasts and monsters. Recruited by the powerful, but distrusted by all.
11) Summoner. These masters of contractual magic form a bond with an eldritch beast or powerful extraplanar being. They can summon avatars of these beings into existence, channel some of their power into magical and effects, and learn rituals to bind even stronger beings into their service. Contractual magic is risky, but often pursued by the ambitious and those with nothing left to lose.
12) Sorcerer. An individual born with the rare gift of mana, they can conjure gouts of fire, storms of ice, rays of acid, and even bend space and time to their will. Many try, but few are able to escape their inborn destiny as weapons of war.
13) Wizard. The scholar of magic. Although not born with the gift of mana, they are studious scholars of magical theory. Through diligent runework, they can produce scrolls of temporary magical effects and eventually produce permanent magical crafts. To a wizard, all magic is merely techniques not yet understood, and they attempt to learn and copy the effects of magic they discover in the world. Wizardry is a poorly regarded art, but those who master it can reach heights of power undreamed.