Want to raise a bilingual child. Should me and my wife speak different languages to our newborn right from the beginning?

Yes - I have several friends who have done so. I also have a set of friends whose children learn three languages this way. One parent speaks french, the other Spanish, and they live / school in an english speaking environment. You may go through a period where they balk a bit, but with persistence, it will keep the language alive until they rekindle interest.