In light aircraft, non-instrument flight, apply (nearly) full aft elevator before beginning the takeoff roll or at some predetermined speed? Consider a small, light, nose wheel tricycle aircraft, something along the lines of a C152 or similar, sitting at the end of the runway ready for takeoff, with no issues and with all pre-takeoff checks completed.

In general, what is the correct procedure for take-off with regards to the elevator and nose wheel?

One instructor I've flown with taught takeoff as apply nearly full aft (nose up) elevator before beginning the takeoff roll. After rotation occurs, accelerate further to and maintain best climb speed, limited by maximum flaps extended speed (which for the particular type I'm flying are identical). This approach has the obvious advantage of getting the nose wheel off the ground as soon as there is sufficient lift for that, and ensures that one can look straight ahead at the runway, not really having to worry about the instruments at all before rotation, but means you need to be careful to not apply too much aft elevator at the moment the nose wheel lifts off the ground (since you don't yet have sufficient speed to actually fly, and by rotating too quickly you'll end up with a tail strike on the runway).

Another instructor, in the exact same aircraft, advocated neutral elevator until around the maximum speed the nose wheel can take, then slight aft elevator to raise the nose wheel, and more aft elevator for lift-off only when approaching speed of best climb. This has the advantage of keeping you near the ground longer during the takeoff roll, but requires keeping pretty close tabs on the instruments (and possibly adjusting from airspeed to ground speed, because the nose wheel is concerned with ground speed which is likely less than the indicated airspeed because the airplane is facing a headwind component). To me, this seems more complex.

Obviously in both cases, after lift-off, the important number becomes the indicated airspeed (a proxy for which can be engine power and airplane pitch), which should be near the speed of best climb to gain altitude as quickly as possible. That's the easy part.

But while the wheels are still on the runway, why would one prefer one style of takeoff over the other? Are there any particular situations in which either is clearly superior to the other, or is it merely a matter of taste?
It's a matter of the conditions you are faced with.

The first instructor was teaching you soft/rough field technique, where the focus is getting as much weight off the nosewheel as soon as possible to minimize its rolling drag on a soft surface. Besides the drag on the nosewheel, the thrust line acting above the drag axis of the mains on soft ground tends to drive the nose down, so you need to compensate for that as well. The other thing is having the wings producing partial lift from the nose being high also helps reduce the effect of the soft ground.

You might also use this technique if the surface is firm but has a lot gravel, that can get sucked into the prop, and you want the prop as far away as possible while the airplane is moving slowly.  I'll start a run on firm surface with loose gravel with the nose held high but let it come down a bit as speed is gained and there is less tendency for the prop to pull rocks up into it.  

Thing is, you need the nosewheel for steering control until the rudder becomes effective, so you give up a lot of potential directional control with tail down technique early in the takeoff, so you only use it to the extent you need to.  Besides directional control, the nose in the air condition is very draggy and can delay acceleration, actually extending the takeoff run.

There are basically 3 procedures that I follow:


Soft/rough field - tail low all though the take off to keep weight off the nose wheel and as much weight off the mains as possible.  You may use flap in this case when you wouldn't ordinarily for the same reason.  You stay in ground effect to accelerate before climbing.
Firm but short field - tail low late in the takeoff and rotating early so the airplane gets to flying speed already at its takeoff pitch attitude. This is to have the airplane lift off at the earliest possible point and may include use of flaps that aren't normally used.  You stay in ground effect to accelerate before climbing.
Normal takeoff - elevator neutral or only slightly nose up, for best steering control and acceleration until rotation at the normal rotation speed.  


Students using different instructors always discover quite a bit of variation in techniques as instructors apply their personal preferences.  A perennial problem in the industry.