Four weapon using classes and three spellcasting classes.
Fighter, Paladin, Ranger and Rogue. All four base classes should be able to have STR builds and DEX builds, and have no spellcasting. However, each of the four should have a single subclass that grants spellcasting (either 1/2 or 1/3 casting.) Subclasses are selected at 1st level.
Bard, Cleric, and Wizard-- one that uses CHA, one that uses WIS, and one that uses INT. However, I'd also put in a Variant rule in the game that allows each of their subclasses (College, Domain, and School) to change what their primary ability score is. So College of Valor would use CHA, but College of Lore could use INT. A Life Domain cleric uses WIS, but a Knowledge Domain cleric uses INT and a Trickery Domain uses CHA. A Divination School uses INT, while a Necromancy School uses WIS and an Enchantment School uses CHA.
All three base classes would be spellcasting first and foremost, with each one having at least one or two subclasses that allows for martial combat. So College of Valor, War Domain, Evocation School could all grant some bonus weapon and armor proficiencies as part of their 1st level subclass abilities.