In the Movie:
-Zefram Cochrane is a human.
-The first aliens to be met are Vulcans (or Borg, if you wanna really nitpick)
-Warp drive is invented before first contact.
-Zefram Cochrane is fairly old
In the TV show, reference guide, technical manual and writer's bible:
-Zefram Cochrane is Alpha Centaurian.
-The first aliens met are Alpha Centaurians.
-Warp drive was a joint venture between humans and Centaurians AFTER a sub-light sleeper ship carrying humans traveled from Earth to A.C.
-Zefram Cochrane DIES IN HIS TWENTIES!