For story I'd recommend the Mass Effect series, the first 2 Bioshock games, Dragon Age Origins, Morrowind/Oblivion, Divinity: Original Sin, the Witcher series (3 being the best by a long shot IMO) and Wolfenstein: the New Order. Enslaved: Odyssey to the West is also a very good character/story driven game.
There's dozens of others that come to mind, but these will suffice.