Usually stories are told in Past Tense: "So Froggy put on his socks, pulled on his boots, put on his hat, tied on his scarf, tugged on his mittens and flopped outside into the snow - flop, flop, flop."
Given the pictures of this story, pointing to one of them I would describe it to my child as: "Froggy is putting on his socks." Describing the next picture would be: "Froggy is pulling on his boots." So, picture by picture, it sums up to a story telling in Present Continuous.
In other languages, there is often a possibility to use a Present Tense to tell a story. Is a Present Tense one of idiomatic choices for story telling in English? If yes: which one - Simple or Continuous/Progressive? Or maybe both?
In case of the example above, could I rephrase the story as: "Froggy puts on his socks, pulls on his boots, puts on his hat..."?