World of Warcraft doesn't require very fast internet. It only consumes 5656kb/s. If it’s just you using the internet, you should be OK with 50mb/s connection or higher which is relatively standard for multiple people. Going 3mbps would let you play without any lag.
See the minimum and recommended system specifications for World of Warcraft for Windows and Mac here. Note that the minimum system requirements for World of Warcraft may change over time due to potential programming changes.
World of Warcraft's developer, Blizzard Entertainment, tweaked some of the racial attributes in World of Warcraft: Warlords of Draenor, the game's latest expansion. Know what WoW can tell us about race in real life at NPR.