Some of these are great games but would take a while to get into, like Arcanum, Silent Hill 3 or Final Fantasy X. Don't go into them with a "backlog clearing" mindset, it'll diminish the fun.
That being said, Limbo and Braid are short and really good.
Beyond Good and Evil is one of the most charming video game experiences I've ever had, and is good from start to finish.
Resident Evil 4 is a fantastic experience, play that as soon as you can. The Resident Evil remake on Gamecube is really good as well, but is slow at times.
Metroid Prime is always good, haven't played the Wii trilogy but I heard it makes good use of the controller.
Deus Ex is possibly the best single player experience of all time. Play that when you're ready for a paradigm shift.
If you want something with immediate payoff though, try Amnesia: The Dark Descent. There's life before that game, and life after that game. What happens in the middle, we don't like to speak about.