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.
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.