Originally Posted by gescom
You made the right choice. Although I haven't played Madden 08 I also heard that it was amazing. The games I think you should have on your list...
Call of Duty 2,3 & especially 4
Gears of War
Rainbow Six Vegas
Oblivion Elder Scrolls
That's 11 games that I have either gone through or at least played a little of and I couldn't recommend them more. Some of them can be had really cheap. In fact you can probably pick up copies of Call of Duty 2 & 3, Rainbow Six Vegas, Obvlivion for a combined $100 or less. Those 4 games are all fantastic and will get you off to a great and economical start.
If you just want to dive into the best of the best then without question I'd go for Gears of War, Call of Duty 4 and Bioshock. Hands down the 3 best shooters available on the 360 and despite all being shooters they are all a unique gaming experience.