The story is not just like a story. You have to pick up all these valuable gems which later become part of the system of Vedanta. They all come from here, from this one and from other Upanishads. We'll keep coming across similar teachings. But the actual teaching of Vedanta will start later. It's something like Bhagavad Gita. If you see the Gita, the first chapter is just the background or Juna's problem. Actual teaching by Krishna starts in the second chapter. And that too in the 11th, Shloka the second chapters. Shankara Chai is quite impatient there. He gives a fairly good commentary on the story itself
Swami Sarvapriyananda teaches the Katha Upanishad, which is one of the most popular Upanishads. The scripture concerns the story of a young man who goes to the house of death to find out what happens after death. The reply describes the nature of reality and the meaning of life.