Are most speeches or talks more engaging if you start them with a story?

Answer 1

Generally yes. Capturing the audience with either an anecdotal story, or giving a testimony as the majority of a talk will tend to be more captivating than a presentation or lecture on a specific topic. That being said, if the objective of the speech or talk is to inform or teach, adding anything more than a one or two sentence anecdote likely isn't going to be useful.