It all has to do with how close this material is going to be to the camera. If it's far away, then use either a normal or a bump. If it's close, use a displacement. I've outlined the pluses and minuses of each way.
Bump map: Has position (X Y), and amplitude (black->white).
Advantages: Quick to make, quick to render.
Disadvantages: Can create banding if pushed too high. Pushes the pixels of the shader around. Does not actually move the geometry. Can not be seen from the side of an object. (Ex. The effect is lost if the camera is not face on)
Normal map: Has position (X Y), and surface normal orientation (X Y Z) mapped to R G B.
Advantages: Fast to render. More precise than bump maps.
Disadvantages: Need certain software to create the maps. Does not actually move the geometry. The surface normal in the lambertian equation (the lighting model) is changed corresponding to the normal map. Can not be seen from the side of an object.
Displacement map: Has position (X Y), and amplitude (black->white).
Advantages: Moves the geometry. Can be seen from the side.
Disadvantages: Slow to render. Sampling settings can be high. Can create banding if pushed too high.
You can also use a combination of the different maps. Many people create mid-resolution displacement maps, then use normal or bump maps to add in the fine detail.
Imagination is more important than knowledge.