How much work do you want to do?
You can get free samples of pressure transducers from
Freescale, and you can build a pitot tube and a static pressure sensor with them. (There are even differential models with two inputs.) You could probably hook those up to any microprocessor with analogue inputs, and translate pressures into velocity using a bit of math (Bernoulli's principle, essentially). See
here, for example.
I've seen these work well enough to read back airspeed on model aircraft (for an autopilot), so you can probably expect decently good results. (I nearly built one of these systems myself, but we managed instead to salvage the sensors from an old version—I just built the pitot-static tube itself.)
On the other hand, for simplicity, try to get your hands on a commercial hot wire anemometer. I don't know whether any exist that can read low speeds reliably, but if you're planning to run the ceiling fan at full speed, I don't doubt that it would pick it up.
By the way, may I assume that you're not aware that this forum is generally used for discussions among members of the
FIRST Robotics Competition community? We'll probably be able to give you general advice, but you're going to find that a lot of answers tend to be centred around the competition challenge itself. Feel free to ask, however.