solar system - Do origin theories imagine each planet to first orbit the Sun very irregularly before stabilizing?

Actually, the sun, planets and other small bodies are all created from the cloud of dust and gas that existed before the solar system. As the gas and dust collect towards the center, the mass rotates and soon an accretion disk forms (which is why the planets are nearly on the same plane).

So your notion of the beginning of the universe is incorrect. It did not start with a bunch of planets (or stars) randomly thrown into space. Also all the stars in a globular cluster are rotating in the same direction; the stars are in orbit in the cluster.

Added:
Yes, they did have irregular movements. It started with a large cloud of gas and dust, some from the big bang, mostly from exploded stars systems. The particles all had different directions and speed.

When gravity influenced enough particles to group and start accumulating is when the mass began to spin (conservation of momentum). The spinning mass flattens out to an accretion disk and planets can start to form (along with the sun).