Many of the games have demos on XBL
Favorites:
GTA4 with the DLC -I can only suggest this game with the DLC. I didn't like the Nico story but never got far into it.
Ikaruga -XBLA $10
Street Fighter 4
Castle Crashers -XBLA $15
Castlevania SotN -XBLA $10
Fable 2
Geometry Wars 2 -XBLA $10
Ninja Gaiden 2 (I like Ninja Gaiden Black better which is downloadable on Live from Xbox Originals but 2 was good) Stores $20
Braid -XBLA $15
Peggle -XBLA $10
Burnout Paradise and Revenge: Both are great. Revenge is quicker to get into and is more direct with a menu driven gameplay. Paradise is an open world environment with objectives besides the races. Paradise keeps getting updates although it has been out for quite some time and it's publisher is *gasp!* EA.
Unfortunately, 360 is riddled with many FPS games. But that's because it's sold so well and devs/pubs know it's demographic. US-Europe 14-30 years old sports/racing/shooters. But the library of RPGs is slowly growing. Some solid ones too from what I hear. I haven't played a RPG on the 360 yet.
The mic might suck. EndWar didn't have that problem with me. I think there is a sensitivity option too on End War when calibrating the mic. I can be wrong. But I know that some mics are defective because I bought a mic and it was defective where I had to deepthroat the mic to have it register anything. I took it back a day or two later but I'm glad I have no gag reflex.