I think Halo 3 has the best online. Assassin's Creed has the best in-game cinematics but no online or co-op. Call of Duty 4 is realistic with modern weapons instead of futuristic or past and rivals Halo 3's online. Splinter Cell Double Agent was turned into more of a shoot 'em up but was still fun for a little bit.
I would get Halo 3 first then Call of Duty 4 or Assassin's Creed based on whether you want to play online or not.
Oh man. So many awesome games in each Category. I love gears of war- #1 . Halo is newb easy shooter. But Fable 2 Is amazing for an RPG. And assassin's creed was amazing for the graphics,size, and ingenuity.
i dont really play taht much xbox 360 but my two favorite games on xbox 360 would have to be gears of war both frist and second, and also assassins creed