Originally Posted by
Fencers
Try out Renekton if possible. He is pretty simple to use, can take a few hits and has great damage. But he has some finer points to his playstyle which reveal themselves as you play him longer.
You want to play heroes with a low barrier to entry but that have some subtle depth to them; Wukong, Renekton and Graves [Ranged] are good picks. Simple enough to start with, but just skillful enough they shine the better you become.
I would stay away from the more tricky heroes such as Fizz, Akali, Olaf, Nidalee or Lee Sin. At least till you have a firm grasp on the game. Don't get me wrong, those are awesome heroes. Though they can be sorta hard for a new player to master. The aforementioned require more finesse in knowing how to counter vs. their inherent weakness/strengths & how best to use their kit.
Playing Annie for a few weeks will teach more about the game than any other hero however. But she's a mage.