Will a first gen Xbox 360 handle game releases from 2011+?
Solution 1:
As long as you don't suffer a catastrophic hardware failure, any game should work fine. In fact new 360s' CPUs clockspeeds are restricted to match the originals so that there will be no processing differences between the models.
I would recomend that you get a hard drive for the 360 and install any game you play on it. Loading from the HDD significantly improves game performance.