Tada!
Yes, it's messy, but that's because the game itself has a bit of a messy class tree.

Here is a list of how much total XP is required to unlock each class (across all required classes for that unlock):

Everything: 6800
Gatekeeper: 3050
Spell Archon: 2050
Enchanter: 2000
Shiftcloak: 1650
Mechanist: 1400
Unmaker: 1300
Balancer: 1200
Breaker: 1150
Blade: 1100
Sorcerer: 500
Guardian: 450
Sharpshooter: 400
Sage: 350
Brawler: 300
Rogue: 250

I have a few notes that might be of interest as well.

• Each base class has 6 other classes descended from it, except Scholar, which has 7
  
• Scholar also has the most classes that are uniquely descended from it (and not from the other base classes): 5, compared to 3 for Warrior and Scout.
  
• No class is descended from more than 2 base classes. Blade and Shiftcloak are descended from Warrior and Scout, Spell Archon is descended from Scout and Scholar, and Enchanter is descended from Warrior and Scholar.
  
• Gatekeeper has the most prerequisite classes, at 5.
  
• It would cost 6800 XP to unlock every class on a single character, which is surprisingly doable. In my last game (which was not a 100% clear), my characters earned 16000-17000 XP each.
  
• If you did the above, you wouldn't need to earn any XP as a Beaker, Enchanter, Gatekeeper, Mechanist, Shiftcloak, or Spell Archon - none of those classes have descendants.
  
• In the game's files, the icons for Warrior and Spell Archon have different names: Knight and Spellslinger respectively.
  
• There's one additional class in the game, called Gatemaster. It can't be unlocked by players, but Ekrast has it.