Its hard to do all of it leveling with a signle character, normally you will outlevel the expac long before you finish it. But it is the best way to experience the dungeon lore for each.
Leveling you start at Cata no matter the race from 1-58, then you go to Outland (BC Era) 58-68, Northrend is next for Wrath of the LK 68-78. Now you run into the issue of Pandaland and Cata overlapping level wise chronologically you want to do Cata first then Panda. After that is Warlords and then legion which catches you up.
For the raid lore your going to need your max level character and just look in the raid journal, the order you see them is the order they released giving you a chronological order of those too