Old Content Story/Cutscenes

Hey guys, first time posting so i'm not sure if this is the best place to ask.

So, I've come from retail and I wanted to learn the story from pre-Cataclysm so i can better understand the stories found in WoW. I've downloaded WotLK from here, I've started playing and began to wonder. Will i be able to see the cut scenes, story and events leading up to Wrath story line if i play on a Wrath server? or would it be better to play Vanilla server -> Burning Crusades -> then Wrath?

I wanted to avoid having to play on three different servers just to get the story as i would find a race/class that i want to main, and have to slog through level 1 - 60 then 1 - 70 and so on just to get to the new story of each expansion. Its a minor complaint and I'm willing to do it, but if i can view all the cut scenes and stories leading up to and beyond Wrath on a Wrath server then that would be awesome!

Thank you for your answers!

Cut scenes kind of got their start in wotlk and progressed from then. I'm sure a quick search on a famous video site would land you a nice compilation.