It really depends, as a favorite style I would say Action/Adventure, like God of War. But of course there are plenty of types that I like, the only ones that I don't like are sport games. Recently the best games that I played was The Walking Dead Season 2, Tomb Raider, Rayman Legends and Xcom.
I bought Bioshock Infinity but didn't play it yet Oo, need to trade my computer first…
And since you like deep games with good histories, I really recommend you to play The Walking Dead, it is really amazing, I wasn't excited to play because it is a point click, but after playing it I can say it is one of the best games from this generation.
The others I liked because they were really fun to play, they were those games that are hard to stop playing, hehe.
I also recommend Alan Wake, it is really good.