If you'd like to get into the lore of the game and to understand what is all that is going on around you, I'd suggest starting with the chronicles.
http://readcomiconline.to/Comic/World-of-Warcraft-Chronicle-Vol-1/Full?id=106975
You can find most of the chronicles as E-books/audio books starting around $20 per, but here's the first book, free.
My advice: Be sure to READ the texts of dialogue of the quests, not just about the rewards you'll receive from them. The game is beautifully in-depth and passionate with the lore. If you pay attention to the quests and the reasons as to why you are doing them story-wise, you'll grow to be attached to certain characters/ subsequent stories of the game, much like a book. There are many, many major and minor plot lines and personalities in the game, enjoy them.
#2: Check the calendar as well, there are holiday/special events that occur for you to partake in, incredibly fun on the side when you're a little burnt out - children's week just started, visit the orphanage in Orgrimmar if horde or Stormwind if Alliance and play with some orphaned kids! Hope you enjoy the game as much as I do.