Want a caster with unlimited magic? That's all the full casters as they all have a handful of cantrips that can be illusions, low power, dancing lights, minor skill boosts, make holy water, etc. Use them at will and ad noseum. Also, casters can have semi-unlimited magic in the form of rituals. They take +10 minutes but you don't use spell slots. Many divinations are rituals.
Want a Barbarian that can commune with their ancestors or listen to the spirits of the land? Maybe a thief that can cast detect magic or identify on their ill gotten goods? A feat can give them ritual casting.
How about a paladin that likes to party and can be impulsive? Or maybe you want to be batman, all full on vengeance? How about a "big picture" paladin who worries about demons, devils and other outsiders so they don't sweat thieves? Or, you know, glowy sword, righteousness, that's still cool. And all paladins get a "smite" ability to add a fistful of d8s to attack damage (powered by their spell slots) Does your paladin want to have a pegasus, dire wolf or a rhino as a mount? That's a thing they do now.
How about a bard that's not a punchline? Some of them can be on the front line, sword, shield and armor gleaming. Others are too pretty to look at and ooze fey charm. Some make wizards look like spellcasters with lots of power but don't truly know the secrets of magic.
Wizards do have a number of secrets to spellcasting. They have an array of spells they can choose to prepare for the day from their spellbook , but they can choose what slots to use when they cast them. Prepare fireball and cone of cold, then decide if you use your three 5th level spell slots on 3 fireballs, 3 cones, 1+2, 2+1, whatever. Plus they get a ton of ritual spells and solid cantrips.
Wizards also have decent subclasses. A warmage can manifest a form of shield innately, diviners can influence fate, abusers wind up with a kind of force field, and conjures can whistle up items from thin air. None of which use spell slots.
Maybe you want a character with a draconic, demonic, fey, or other Outsider background without being a tiefling or asimar. (Which you could do too) Sorcerers have some supernatural bloodline and get pseudo-innate casting and various manifestations of their ancestry.
Or perhaps you want to cut a deal with a being of Power. Maybe your parents cut the deal for you. Maybe now you can hear the kitchen knives whisper, your sword is your best friend and it comes when you call it. Or you have the ability to breath water, never sleep or turn invisible in shadows. A book of shadows might contain mystic secrets and if it's stolen you can dream it back to your side. There may be a demon or even an undead that is your servant. And you get the best cantrip in the game, which does more damage than a warbow but at similar ranges and you get multiple shots.
Want a fighter that can actually be a tactician, enabling the rogue to (sneak) attack outside their turn, the mage to dodge enemies, or just smack the sword out of some punk's hands?
How about a warrior that knows runes and can call upon the elements to redirect attacks, entangle foes, and just lays the smack down?
Spellcasters of all types get more usable magic at low levels (no magic users with only one spell per day) and they get all their slots back with a full night sleep. Some can even get a handful of spells back with a 1 hour power nap.
Oh and caster interruptions are mostly a thing of the past. Only a caster with counterspell can block a spell and not all classes get it.
Skills are also more sane than non-weapon proficiencies and rogues get a lot of them, letting them be more than pick pockets and door openers.
And from a campaign sense, have you ever bemoaned how weak you were at 1st h 2nd level but how the campaigns tend to stop at 12th level because you got so powerful you can kill adult dragons? Problem solved! In 5e everyone at 1st level is competent, full casters have multiple spells per day (plus cantrips and rituals), all characters get max hp at first level and the smallest PC hit die is d6. (14hp fighter-1? Almost always! 7hp mage-1? Yeah, most of the time!)
Downsides (unless you complained about 1e PCs getting too powerful to be challenged):
Do you want to play DnD on "hard" mode? All monsters have 2x more hp than 1e. (Kobolds 2.5 vs 5, trolls 33 vs 84, red dragon 88 vs 256, etc). PCs get more hp too but it's more like 50% more (though mages get a bigger relative boost as they use d6hp)
Your weapons will do about the same damage as 1e so that's a bummer. Good thing you get tactics and Smite and such so that claws back some of the warrior-types losses.
Spells are about 50% more powerful when you get them but they don't level up automatically. So +50% means you do proportionately less damage when the baddies have +100% hp. That 10th level magic user killing a 33hp troll with a 10d6 3rd level fireball? Yeah, doesn't happen. A 7th level delayed blast fireball you nursed for a minute to get to 22d6 (77hp) won't do it as trolls have 84hp. It takes a Meteor swarm (40d6/140gp) to one-hit a troll. Forget ever having 10 troll-killing spell slots.
Most spells with a duration require you to concentrate and you can only do that on one spell. Very few combat spells with a duration of more than one round do not require concentrations.
Almost all spells with harmful effects and a duration also allow a save each round. Oh and when you take damage, you can lose that concentration spell, freeing something from Charm or Hold or banishing Invisibility.
Starting at 9th level you have fewer spell slots in 5e and at no point do you ever get two 8th or 9th level spells.
And while spell interruption doesn't exist (aside from breaking concentration and Counterspell), many of the "legendary" creatures get Legendary Actions and/or Lair Actions which can include deciding to automatically save against a spells. Better get used to that one Disintigrate spell you have from 11th-18th level doing neither diddly not squat. Well, maybe if you first exhausted your one 9th, one 8th, and one 7th level spells first. Legendary Actions are finite at least.
