Expanding a bit on your other answers:
The Lorentz force, due to the electron's motion through the field, is always perpendicular to the field direction, and generally won't steer your electron towards or away from either pole.
As Floris points out, the electron also has an magnetic dipole moment. In a nonuniform field, a slowly-moving electron will find its spin aligned or antialigned with the local direction of the field, and will feel a force
$ F = \mu\nabla B $. However the electron magnetic moment $\mu_e\approx$ 60 $\mu$eV/T is quite small, and for a real electron in a real apparatus subjected to volt-scale stray potentials, a few microelectronvolts of magnetic steering is a negligible correction to the overall motion.
While the dipole-field interaction is usually negligible for the electron, it has been used to build magnetic traps for neutral particles.
Edited to add: if a charged particle (either sign) is steered towards a region of strong magnetic field, such as the field near a magnetic pole or a cusp on a material magnet, the Lorentz force conspires with the rapidly-changing field direction to reflect the particle from the pole.