Add in everybody else vacationing at the time, and that's probably pretty accurate of WOW Classic. Retail doesn't possess the"original story", because the lvl 1-60 questing was completely revamped in Cata, but there isn't really a big overarching narrative in WOW Classic, therefore I'd go with retail. The story is sort of a mess though. Chronologically it goes like this: BC (60-80) - WotLK (60-80) -"Vanilla" (1-60) - Cataclysm (80-90) - Pandaria (80-90) - WoD (90-100) - Legion (100-110) - BfA (110-120).So it is kind of messy to find a fantastic understanding of the narrative by simply playing, especially since classic gold wow you're gonna be skipping a lot of zones if you would like to level. I would just suggest viewing some Youtube videos or reading up on it.
Kinda nuts is a little bit of an understatement. Timelines in the game are a clusterfuck that is certified. You will begin from the south-west zones, where a few quests were altered to signify the cataclysm and a few were not. That means you be in Cataclysm age in rather and vanilla era. Then you'll zoom forward/backward to MoP or Cata, then again into Wrath or TBC. It will get somewhat more coherent then, if you can predict the crazy retconning and alternative universe jumping of WoD and Terrible nonsensical"storytelling" of BfA coherent. They began placing plot points in books and other media without describing them in-game, so you're going to be missing out on a lot by playing WOW Classic.
The Chronicle series along with youtube vids are def the way to go if you'd like to acquire a semblance of a narrative out of what since WOW Classic. WOW Classic, meanwhile, does not actually have a story. It's more of a set of vignettes that flesh out its inhabitants and the world. To put it differently, it's about worldbuilding, not storytelling. Vanilla kinda felt without a singular focused direction. It was an opportunity to run around in the world of the RTS games and research the areas that are relevant and meet a lot of the significant characters and such.
There are some vital events for some of the figures, but you won't be terribly lost if you don't encounter it moving. Again, the issue with following the story isn't that you overlook important things but that the storytelling is disjointed and incoherent. If you liked WC3 and need classic wow gold sellers to explore that world or if you like worldbuilding over storytelling (I do, and again, I believe Blizz does a far better job with all the smaller vignette fashion than telling a grand narrative), then proceed for Vanilla. Read Chronicles, if you would like to acquire the strokes of the significant events throughout the history.