EridanMan wrote

Standard Takeoff-
Flaps per POH (usually retracted), accelerate smoothly to Vr, put the
aircraft into Vy attitude, let the plane climb away on its own.

YES

Short Field Takeoff-
Flaps per POH (usually 1 notch or so), accelerate quickly to Vr, put
the aircraft into Vx attitude, let the aircraft climb away on its own,
drop the nose and take Vy attitude as soon as passed obstacle
altitude.

YES

Soft Field Takeoff-
Flaps per POH (usually 1 notch or so), accelerate to Vr, pull back
firmly to get the aircraft into ground effect, then lower the nose
again once in ground effect and let the aircraft accellerate to Vx or
Vy, depending upon whether or not there are obstacles to clear.

NO....The following is from the FAA's Airplane Flying Handbook 5-10

TAKEOFF ROLL
As the airplane is aligned with the takeoff path, takeoff
power is applied smoothly and as rapidly as the powerplant
will accept it without faltering. As the airplaneaccelerates,
enough back-elevator pressure should be
applied to establish a positive angle of attack and to
reduce the weight supported by the nosewheel.
When the airplane is held at a nose-high attitude
throughout the takeoff run, the wings will, as speed
increases and lift develops, progressively relieve the
wheels of more and more of the airplane’s weight,
thereby minimizing the drag caused by surface irregularities
or adhesion. If this attitude is accurately maintained,
the airplane will virtually fly itself off the ground,
becoming airborne at airspeed slower than a safe climb
speed because of ground effect. [Figure 5-9]
LIFT-OFF
After becoming airborne, the nose should be lowered
very gently with the wheels clear of the surface to
allow the airplane to accelerate to VY, or VX if obstacles
must be cleared. Extreme care must be exercised
immediately after the airplane becomes airborne and
while it accelerates, to avoid settling back onto the surface.
An attempt to climb prematurely or too steeply
may cause the airplane to settle back to the surface as
a result of losing the benefit of ground effect. An
attempt to climb out of ground effect before sufficient
climb airspeed is attained may result in the airplane
being unable to climb further as the ground effect area
is transited, even with full power. Therefore, it is
essential that the airplane remain in ground effect until
at least VX is reached. This requires feel for the airplane,
and a very fine control touch, in order to avoid
over-controlling the elevator as required control pressures
change with airplane acceleration.

"popular" takeoff-
Flaps per POH (usually retracted), accelerate to Vr, pull mains off,
lower nose in ground effect, and accelerate to Vx or Vy as necessary in
ground effect (even on a hard surface runway) before climbing away.

NO

Bob Moore
ATP CFI(I)
PanAm (retired)