My two cents
Here are a few of the storylines I've used in the past to present ideas. In case of doubt, go with the Q&A as it's the one that feels the most human and conversational.
The Q&A
A slide structure that makes your presentation more conversational where you use questions as the chapters of your presentation. You can even use “provocative” questions or remarks like: "Why the fuck should I care?" or "This is too expensive!", because it's smart to answer the nasty questions before people ask them themselves.
The Pitch Deck
A slide structure used by Silicon Valley startups to raise money. A pitch deck helps you make sure that you say all what is necessary to convince. I like to use the 10 slides structure by Guy Kawasaki, ex- chief evangelist at Apple.
The Meet John
A slide structure to help people empathise with the customer. In this structure, you tell the story of someone who is affected by what you are presenting. Why not present in a user-centric way if we already design in a user-centric way?
The McKinsey
A slide structure is used to make 500’000$ with one presentation. This storyline recognises that top managers and decision-makers want the answer right away and no bullshit. So we lead with the answer. This is the structure that the management firm McKinsey uses for many of its presentations.
The Steve Jobs
A slide structure is made to help you memorise and create excitement. In this structure, we use the power of repetition to help people memorise, and we use the power of surprise to create emotions. This slide structure works well because it creates an emotional high with the surprise of the "One more thing" and again gives the key information at the end.
That's basically what we can learn from the cognitive bias: Peak End Rule that says:
“People judge an experience mostly based on how they felt at its peak and at the end of the experience.”
The A.M.A. or Ask Me Anything.
A slide structure for the busy executive and difficult audiences. Here we outsource the decision of choosing what we should show, build a minimal well-designed presentation, and keep a bunch of less well-designed slides hidden if people want to know more about a specific topic.
The At Nauseam
A slide structure to ensure that people go from hating an idea to accepting it. This storyline recognises that people first hate new ideas and need to see them a few times before they can like a new idea. This is based on the repetition cognitive bias:
"“Repetition bias is a cognitive bias in which there is a willingness to believe what we have been told most often and by the greatest number of different of sources.”
This structure is commonly used by marketing and branding agencies when pitching a campaign or brand identity. Usually the type of feedback you get at the end of such a presentation is: "I wasn't sure at the start, but now the idea has grown in me! I like it!"
The 4P’s
A slide structure to prove that your idea has value. In this structure, we recognise that people need proof before they say "yes" to our proposition.