How long did it take for Earth's magnetic field to first appear? Merely what the title states. My knowledge of geography/geology/*logy is limited to high-school, and some snippets, and snatches of conversation.

As I understand Earth's magnetic field is attributed to the bi-layered nature of it's core. Proto-Earth probably did not have a magnetic field. Apparently much later Earth's core cooled enough to separate into two layers - causing the field to appear

How long did it take for Earth's magnetic field to first appear? 
As a corollary, did water appear first on Earth, OR did the magnetic field appear first?
The age of the Earth's magnetic field could be as old as the existence of the physical conditions capable of generating a magnetic field. Because we believe the geomagnetic field originates from the liquid outer core, your question could be restated as: When did the Earth form a liquid core?

How the Earth's core formed is still not well understood and the area of research is referred to as planetary differentiation.