"I got out of the house..." - it sounds as though it was difficult to get away. Perhaps you were delayed by phone calls, or you were rather late getting yourself organised that morning.
"Headed out the door..." - it sounds a little strange to me if you are describing a routine departure from home. Maybe you were upset and made a rush for the door, or anyway you left hurriedly

. We usually talk about being headed for (towards) a destination: I left home and headed for the train station.
"I left home..." sounds neutral, unlike the other two versions.