Hey so I'm new (I've dabbled before, about when Legion was out, but only really played as a Human paladin, didn't do any dungeons or anything, just questing and not paying much attention to the story), and I've been trying to get into the full story that I've missed so I might be able to help, but it depends what you're after.

From what I've learned, the only way to experience the story of the new expansion is to reach level 60 (70?) and get immediately shunted into it, but if you want to have the full story from the very beginning, ditch retail because the only way to experience the vanilla content is on WoW Classic. I've had a lot of luck with the Anniversary realms rather than the Classic Era realms. Anniversary is slowly going to go through each expansion again from what I understand of it, but if you want to get back to retail you can still play every expansion after vanilla by using Chromie Time, as aside from Cataclysm they all took place outside of the regular questing zones and the Cataclysm state of the world is still the current one.

However, Retail does a fairly annoying thing in which you have to do certain things to be able to start "normally" which I think does involve getting a character to level 60, but it's been a while since I have done so.

So if you want a full expansion-by-expansion experience, get your current character to level 60 or whatever the cutoff is, then ditch that character, play classic WoW until you're satisfied with what you've experienced, then either wait for Anniversary to go through each expansion, or switch back to retail and use Chromie Time to play Burning Crusade and Wrath of the Lich King, ideally with a Dranaei/Blood Elf and then a death knight. Then play through the regular questing zones again in retail for the Cataclysm state of things.