But, actually, he chose a stag because it was large, powerful, and fast. It could survive a werewolf attack (assuming the worst case scenario happened). When the Marauders told Remus they were animagi.
Beyond the Veil by *Avender on deviantART Sirius Black and James Potter reunited again! So Harry saw Kings Cross because that was where he could escape from the normal world to Hogwarts. Sirius escaped from Hogwarts to his friends.