What three things did John see in the beginning of his journey in "By the Waters of Babylon?"
The three things that John sees in what could be called the beginning of his journey are an eagle, three deer, including a white fawn, and a panther. John believes that all of these are important signs.
At this point in the story, John has not truly begun his journey. Instead, he has told his father about his dream about the river, and the Dead Place and all the gods walking in that place. His father then told him that it was forbidden to go east, to cross the river, and to go to the Place of the Gods.
So John goes off to start his journey, but he really has not completely decided where he will go. So he fasts and prays and hopes for guidance. This is when he sees the signs. First he sees the eagle. It flies to the east. Then he sees the deer. They are also moving to the east. Then he sees the panther leap on the white fawn. John kills the panther with one arrow even though that is very hard to do. Taken all together, these three things indicate to John that the gods approve of his idea to go to the Place of the Gods. As he says,
Then I knew I was meant to go east—I knew that was my journey.
So, the three things that John sees are all (in his mind) signs from the gods. They are an eagle, three deer including a white fawn, and a panther.