The only thing that a "new" player really needs to understand is that the story of WoW is tied to the CURRENT expansion. As long as you're still slugging through the lower levels, a lot of things aren't going to make sense. Partly because you're coming in halfway through the history of the story, and partly because the speed of leveling(even without heirlooms) means you'll be skipping around the story quite a bit.
I could definitely see how that would be offputting to someone who's looking for more of a linear story. My advice would simply be to tell new players to watch a couple of lore videos that cover the lead-up to Legion, watch the opening cinematics. And if they're REALLY interested in story, to go read the "Illidan" novel. They'll have all the context they need at that point, without having to slog through the 1-100 "experience".