The Hall Effect is simply an application of the total force law for charged
particles:
If a magnetic field is applied perpendicular to a strip of metal which
is carrying a current, then the electric field in the metal points
in the direction of current flow, and by paying close attention to the
signs of q and 
in the formula above, it is easy to discover that
the magnetic field would push positive charge carriers toward one edge
of the strip and negative charge carriers toward the other.
This makes it possible to tell whether a conducting strip has positive
or negative charge carriers by measuring the electrostatic voltage
between opposite edges of the strip.
There is no sense in trying to memorize special cases; just think carefully
about current, electric field, and the motion the charge carriers and
use the total force law.