Braid is really good, it has some awesome time based puzzle and a wonderful presentation. Be aware that the game is extremely short though. You'll finish it in a few hours. It's not necessarily a bad thing since the game relies heavily on its quirky level design, and it's a puzzle game at its core, so making it longer wouldn't have done much good if it was with anything than more clever puzzles. Since you're short on points, it might enter into consideration.
Portal is another awesome puzzle game, but maybe you should consider getting it on PC. That said, Portal works pretty well with a pad. Like Braid, it's a pretty short game, but it's longer (5-6 hours?) and you can definitely get a lot of playtime if you get into the challenge rooms things.
Lumines is good, but not the 360's dpad. I strongly suggest you to get it on any other imaginable machine or to get a controler with a decent dpad.
Psychonauts is not a very good video game. But it's still a very good experience because the universe and writing is awesome. But maybe you should try to get a second hand Xbox copy of this game. I'm sure you can find a really good deal on eBay.
I can't comment on Castle Crasher since I can't stand beat-em-all for more than 2 minutes.
I strongly suggest Geometry Wars 2, Megaman 9 (but like Lumines, the dpad can be troublesome, but Megaman isn't about super twich reflex or controls, it's more about not acting like a moron and figuring out what to do than executing it). Shadow Complex is also pretty awesome, not Super Metroid awesome, but good enough to be compared.