Tell me about this series because I had never given the Call of Duty games a second glance, but this trailer blew me away.
Well, before 4, it's always been a game about World War 2. Honestly, just know that Call of Duty 1 and 2 have some of the best fire-fights in any fast-paced FPS with easy controls and great multiplayer. 3 was pretty boring just because IW didn't make it, but it's changed with 4.
You'd be fine by just starting at 4, to be honest. You can probably find 2 somewhere for dirt cheap for your 360. It's still awesome.