Classic will be coming out (supposedly) this summer, so you can experience the game as it originally was. Your current character will not transfer though, as it will be treated as a separate game, so you would have to start over with a fresh Classic character. I will also say that Classic is a much more difficult and tedious iteration of the game, so it could be very daunting for a newer player who is used to the current retail version.

In the current version of the game, after Cataclysm, all the original zones were altered. Everything was "updated" and the way it was when the game came out no longer exists, which is why you're seeing references to the Cataclysm in early zones. All the later expansions content is pretty much entirely the way it was upon release other than the fact that it all scales to your level now. Story wise it's all pretty much the same as it has always been.