I second @SirianaSims question. What do you mean by normal? Can you give me an example of something abnormal?
Also, are you talking about stories to read and let's plays to watch, or do you want to play something yourself?
I've personally tried out two new legacy challenges in the past year and I've had fun with both. I'm currently working on an Aspiration Legacy. You start out with a Founder and help them get started with the Grilled Cheese aspiration. The rest of the aspirations go in alphabetical order, with multiple family members participating, once you grow your family.
I also completed an legacy I created where each generation represents a different year of Sims 4 content, and the heir is challenged to use game play from their year. Both of these legacy challenges might be too normal for your tastes, though.