We were then told that these are unreliable and therefore should use stepper motors.
"Unreliable" how? If all you're doing is driving a vehicle forward, a DC motor is fine. If you need precise control in position, then a stepper motor is better, but for general locomotion, a stepper is actually worse, because you have to tune the step rate to the load/speed of the vehicle.
There are also servos. As mechanical engineers, you probably should know about those :-) Servos are motors with additional encoders that tell you exactly how they're currently rotated, so you can get a very good reading on what's "actually" going on. The simplest form of servo is the "hobby servo" that turns +/-90 degrees or so and is used for remote control toys, but industrial servos can rotate arbitrary amounts and keep giving you good readings.
For a stepper motor, you need a "cadence." It's all about magnetics. Assuming you know how a magnet-with-coils motor works, think of stepper motors as one set of up/down coils, and one set of right/left coils (for a permanent magnet/axle going hither/yon.) Now, to spin the magnet, you want to energize the coils so that the magnet rotates first straight up, then 45 degrees clockwise, then 90 degrees clockwise, then 135 degrees clockwise, ...
You create this cadence by outputting to windings A (up/down) and B (right/left):
A: +, B: 0 == top
A: +, B: + == 45 degrees
A: 0, B: + == 90 degrees
A: -, B: + == 135 degrees
A: -, B: 0 == 180 degrees
A: -, B: - == 225 degrees
A: 0, B: - == 270 degrees
A: +, B: - == 315 degrees
As long as you run the motor through each of those states in turn, with some appropriate delay between each to compensate for inertia/speed, your motor will run smoothly. I e, to go from 90 degrees to 225 degrees, clockwise, you have to run the motor through the states 90, 135, 180, 225, with a small pause (several milliseconds, typically) between each transition.
Internally, the stepper motor actually has what amounts to many little magnets offset by a few degrees, which is why you get hundreds of steps per turn, instead of just 8 -- divide the degrees in the table with the appropriate factor for the motor's resolution.
Also, if you want "full torque" at all times, you want both windings to always be energized, which means that you drop four of the eight steps (called the half-steps) -- you end up with the 45, 135, 225, 315 degree entries from that table.