There is some dispute and argument over some aspects; but.

The primary difference is their special abilities and path costs.

Master Alchemist +50% Alchemy Bonus (+50% Money ConVersion on Gems) Path: 10 [Personal Note: I think the Alchemist *should* start with 1 Earth OR 1 Fire]

Archmage 3 Movement, No Feet Slot, Low Dominion Path: 10 I don't like the Archmage much, he's not an arch in my book or much of a mage. His Low Dominion as well makes you have to at least spend 2 Levels in increasing Dominion to even get 3rd Degree Scales.

Great Sage. +Research Bonus, Path:10. He is good if you want him sitting around Researching and casting Rituals, you'll want to forge him some protection items, because a stiff breeze will kill him.

If I had to choose between those 3, I'd choose either the Alchemist (if I planned on Alchemizing) or the Sage (If I planned on going Rainbow).

The Manticore is Physically powerful but starts with no magic and costs Path:50. If you plan on going one path (say Earth, or Astral) he would be ideal.