I don't think you can do the Nightfall until you complete the story (feel free to correct me if I'm wrong, however I think I remember reading that you had to complete the story and level up high enough to unlock Nightfall).
Me? I will be waiting until the brown box truck shows up with my new PS4, then I will hook it up and start updating. Meanwhile, I plan on popping the ce in my xbox one and start running my hunter through the story. It's the first thing I do for every character with every expansion.
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same since my hunter is my 1st character I always do things with him 1st.