Stepper Motors
Steppers are great because they offer essentially 'digital' input that translates to a fixed linear displacement of the robot.
Part Numbers
- Lin Engineering - 4218 Stepper Motor
Steppers are great because they offer essentially 'digital' input that translates to a fixed linear displacement of the robot.
DC motors offer the most design flexibility and design precision at the cost of more complex electronics and software overhead. Any blend of torque/speed can be achieved within the motor's power limits, allowing powertrain optimization for traction/torque.

Servo Motor with Gearhead & Encoder ($155 ea.) Mad expensive but top of the line servo motor with gearhead and encoder for robotics applications. Encoder is 16count/rev, and gearhead is 19:1, so total counts/rev = 304 or 1216 if using the x4 resolution. Dimensions 1/2"D x 2.75"L. Everyone uses Maxon motors in well-funded robotics projects. If donations don't count into the $500 limit, these can be donated directly from Maxon.
These are the best in terms of power density and packaging. However, they require fancy electronics to manually commutate the motors by using hall effect sensors or the back-EMF to infer rotor position.
Encoders are necessary if we want precision control over wheel position/velolcity. If we end up with stepper motors, closed loop control over position would be difficult even if we added encoders.

($6.70/ea, but have samples already) Agilent makes this surface-mount optical encoder chip for mounting directly adjacent to a reflective codewheel. We can use this chip in a couple of ways: 1) if there is a black/white reflective sticker on the actual drive wheel of the mouse, 2) if there are optical encoder disks mounted to the shafts of the wheels. In any case, it would take some good 3D modeling to make sure the encoder chip and the codewheel line up within spec.

($19/ea) US Digital makes this encoder module, which essentially is the codewheel, housing and AEDR chip in a single unit. These are probably the cheapest encoders we'll find.
These can be modified for continous rotation, but have poor precision, resolution and repeatability. Coupled with some feedback, though, they could be a compact and low-cost drive motor.

Pico Servo ($25.50) These are the smallest servos that you can get. If we mount a range-finder device on the end of this thing, we could build a simple directional ranging device. Note: No longer available from Acroname.