Yes, Silent Hill. The music its amazing, even the almost completely ambient first game.
About 98% of games can be installed, but a few titles, especially older titles can't. It'll spit an error message, not crash the machine. Online is completely optional. I don't know any that will drop you out of game if your net drops. Actually, a caveat; XBLA and XBLI games may have varying levels off online DRM. Generally, the console itself is enough DRM.