"Proper" cycling posture on a road bike with drop bars?
Whatever works.  The main advantage of the standard drop bar is that it offers you multiple hand positions and multiple postures.  In a sprint, or driving into a headwind, riding fully on the drops cuts wind resistance, but for less intense riding one of the several hand position on the top bar or on the hoods is usually preferred.  And on long rides the ability to change positions from time to time is invaluable in terms of hand/arm/back comfort.

And there is no one "right" height for your bar.  If you're a real aggressive rider (and young and limber) then a lower bar position may be for you, but if you're somewhat more casual there's nothing wrong with raising the bar (so to speak).  And you may also want to consider adjusting your "reach" by changing the stem -- not everyone's torso is the same length.