Intriguing, and ambitious, idea. This would be difficult given the many different "Flavors" of magic used as a conceit for a D&D style fantasy rpg.
But having been through the headachey hell of formulated my own individual spell lists for my own homebrew...I was asking many of these same questions: "what's iconic? what spell level should this be? Is this a cross-class spell[i.e. should it appear on multiple classes' lists?" etc...
So, I'll give it a shot. Names of these things can be altered to whatever non-class related flavor you want.
Cantrips: Honestly, you could just do a singular "spell" called Cantrip...with the parameters of the ability being allowed to all spellcasting characters, any little/minor spell/flavor effect the player wants to do, anything that could have an offensive application can cause more than d3 damage or have an effect that last more than a single round.
1st level.
Bless: iconic Cleric spell but something that would be useful for any caster: offer a bonus to attack rolls, skill/ability rolls, or saves.
Cure Wounds: iconic cleric but something that would be useful for any caster: Minor healing.
Detect Magic: given.
Light: given.
Magic Missile: the iconic arcane offense. Fluff it however you want to give the appropriate flavor to your character. multi colored darts/shards of [defined] energy that always hits and deals "force" damage.
Protection from Evil/Good - Sanctuary combo: generate a protective circle/field to keep undead and extraplanar creatures (of any alignment) at bay/unable to attack those inside it.
Resistance: resist elemental [fire, cold, lightning, other energy types if you wish/define such things, etc...] damage.
Shield: iconic Arcane spell, but a magical force-field to defend from incoming attack seems fairly universally useful.
2nd level.
Augury: iconic ability of magic-users for as long as there has been magic-users and any kind of divination/religion.
Detect Thoughts: handy iconic divinatory ability, the enigmatic magic guy reading your mind.
Gust of Wind: elemental control, also classicand iconic magical ability across flavors and cultures.
Hold Person: non-damaging offense. useful to any caster.
Levitate: iconic arcane spell, but also iconic magical ability in much literature and myth. Use it offensively, defensively, or for utility. A highly underrated and under-utilized spell from the game.
Magic Weapon/Flame Blade/Smite: cross-class option, make an existing mundane weapon able to strike magical creatures/do additional magical damage. Useful for any caster.
Mirror Image: defensive illusion and classic/iconic magical ability from D&D to Conan to the Voltron cartoon
Spiritual Weapon: Your second level magical energy spell attack that isn't just fire and forget. You need to direct it but can use it to attack multiple targets over multiple rounds.
3rd level.
Cure Affliction: take care of that disease, that blindness, that poison, whatever isn't just HP damage.
Dispel Magic: given. every caster's best friend and most mortal enemy.
Fireball: given.
Fly: classic magical ability.
Lightning Bolt/Call Lightning: given. Does it really matter if its coming down from the sky or flying out of your hands? Hint: No, it doesn't.
Protection from X: a 3rd spell level/beefed up Resistance for either more defense [if not immunity for the spell duration] against a given energy type.
Remove Curse: for all of those fun magical things a dispel magic or cure spell just can't fix.
Speak with Dead: iconic cleric, but traditional witchy/wizardy thing, and literally the definition/original meaning of "necromancy."
4th level.
Control Animals: given classic magical ability for any spellcaster.
Control Water: elemental control.
Cure Worse Wounds: beefed up 1st level Cure spell.
Dimension Door: your first chance to teleport yourself and others, ubiquitous magic-guy stuff.
Freedom of Movement: iconic clerical 4th level spell, but honestly, what caster wouldn't want to benefit from this ability?
Invisibility: make it usable individuals or as a group/area effect. Invisibility is a massively powerful ability granted, imho, far too early in traditional D&D.
Polymorph: turn yourself or others into something else.
Scrying: classic magical ability for wizards, priests, witches, and druids
that should give you a good jumping off point/direction I would be going. How you want higher level magics to work in your game is up to you.