While some study for years to master the arts of magic, the path of the Warlock is temptingly quick and easy...
Warlock - Infernal or Old One
Eldritch Knight & Arcane Trickster
In order to become an Eldritch Knight, Arcane Trickster or other caster subclass the PC must already have the Ritual Caster (Wizard) feat. The quickest way to do this is to be a Variant Human with the Feat at 1st level.
Exception: High Elves have magic in the blood. They may become an Eldritch Knight or Arcane Trickster even without the Ritual Caster feat.
To become a true Wizard the PC must first have 3 levels in a caster subclass such as Eldritch Knight. This means the effective maximum 'true wizard' level is 15.
Example: Bob wants to become a Wizard.
At 1st level he is a Human Fighter with the Ritual Caster (Wizard) feat. He could also have been a High Elf.
At 3rd level he becomes an Eldritch Knight.
At 6th level he can multiclass and become a Fighter (EK)-5/Wizard-1.