if the two forces are equal and opposite … it should stay stationary
Equal and opposite forces guarantee zero acceleration not zero velocity.
Be careful with the term EMF. Its dimensional units are voltage V=J/C. The force part appears when dividing by the distance over which it is applied N/C=J/C-m.
On the mechanical side, when the torque of friction is less than the applied torque, there is acceleration. When the torque of friction equals the applied torque there is zero acceleration (constant velocity).
The motor effect produces torque in response to electrical current. The generator effect produces voltage (back-EMF, \$E_b\$) in response to angular velocity.
On the electrical side, the applied voltage\$E_A\$ sets the maximum angular velocity. The internal resistance will drop some of this voltage by the amount of current flowing through it thus reducing “back-EMF” (angular velocity) attainable. The current (torque) required is determined by the torque of friction at that speed.
the operational speed is reached when the opposing magnetic force (induced by the back EMF) is equal to the motor effect (induced by the current through the armature.)
I disagree with that statement. The “magnetic force[torque,\$\tau_a\$]” is created by the motor effect \$\tau_a = k_{\tau}i_a \$. The back-EMF is induced by the generator effect from the angular velocity.
The armature current, \$i_a\$, thus torque, is actually determined by the lack of back-EMF. $$ \tau_a=k_\tau \frac{E_A-E_b}{R_a} $$
\$R_a\$ is the armature resistance.