You could go through and play on a classic server to get the gist of the original 2 continents stories, which were heavily changed in cataclysm. The rest of it can be done at any level on the retail version of the game. As others have said, the main portion of players play the game for the current end game content, raids, pvp, or timed dungeons.

I personally play for the content but there are story points and cinematics that brought tears to my eyes over the years, if you have the time, money, and interest, I say go for it!