You do not 'unlock' anything in Warcraft III story related. They
come naturally as you continue through the game.
However, I am sorry to inform you that if you do not own the
expansion to Warcraft III: Rain of Chaos, you cannot play the Human
campaign with Arthas found in Warcraft III: The Frozen Throne.
You can purchase The Frozen Throne at a local store in the
popular 'Battle Chest' box, or order it online.