I agree with what's been said already, but let me add in something else: if you are at all technological minded, you can fix the RROD yourself. There is no need to send it back to M$ wasting several weeks when you can have your system up and fixed in a matter of 1 hour.
As for good cheap games......
Earth Defense Force 2017 (~$12) EDF is a third game in D3's popular Simple 2000 series in Japan. It's a budget third person shooter where you kill giant ants, spiders and UFOs. It should by all accounts be awful, but it defies its conventions and is actually one of the best off-line games of the system, espically when playing local co-op split screen.
Prey (~$10) Prey uses the Doom 3 engine and is about native americans and alien invaders. It's story is outright stupid, but its a pretty fun FPS nontheless.
The Darkness, as mentioned
Beautiful Katamari (~$15) Katamari Damacy on the 360. Not much more I can add.
Eternal Sonata(~$20) a very colorful, beautiful J RPG for the 360. It's rather similar to the Tales of series, and goes for much less than Vesperia does.