Question

Millikan's oil–drop experiment measures the charge on individual oil drops. Why would you try to set the electric field force on a drop equal to the gravitational force on that drop? so that the oil drop moves randomly so that the oil drop moves downward so that the oil drop moves upward so that the oil drop remains suspended

Answer 1

So that the oil drop stays suspended. 
at the point where it is stationary, its weight and the force on it due to the field are equal . so you can work out any detail you need

Answer 2

Answer: so that the oil drop remains suspended

Explanation:

Millikan's oil  drop experiment was used to determine charge on electron. The charged oil droplets were suspended between electric field to balance the gravitational force and drag force.

The electric field is generated by applying potential difference across two parallel metal plates. The oil is sprayed which gets charged due to electric field. The field can be controlled by altering voltage difference across the plates. Oil drops reach terminal velocity when gravitational pull and drag force is balanced by the electric force.

The balance equation helps to find the charge on the oil droplet.