What type of photo sensor/light combo best for detecting a falling drop of water?
Initially, I'd try a narrow angle visible light LED and phototransistor, and set up the phototransistor in 'line of sight', maybe inside a tube to reduce the chances of refraction or reflection from the droplet effect the sensor. Something cheap and simple like an old pen body 

The rationale is the visible light LED would make it easy to set up. Infrared (IR) can be awkward because it's invisible. If it works well enough, then it's okay. If not, move to IR. Assuming you make a stable mount for a visible LED, say a 5mm hole, an IR emitter should fit in the same place. 

You might find that reflection from the water droplet, either above or below the trigger point, needs to be dealt with.

A phototransistor would be good because the change in output, with a resistor in series, may be enough to directly trigger a digital pin. The AVR/Arduino ADC is quite slow, about 10ksps, so try to avoid it if you want high precision.

A phototransistor can typically respond in under 20µseconds, so it should be fast enough if the drip has fallen only a few metres. This is significantly faster than the AVR/Arduino ADC.

Most AVR/Arduino's include a comparator, so it may be used to detect the phototransistors change, and ensure that is adequate to detect using a digital pin. 

Edit: One of the comparators inputs would come from the connection between phototransistor and its resistor, the other comparator input sets the 'trigger' voltage. That can be adjusted using a potentiometer as a voltage divider, so the threshold could be tweaked manually to get a good result.

Flashing the emitter is to avoid ambient noise. The sensor is 'sensed' when the emitter is on and off. However, this is most useful when using the sensor as an analogue device. Ideally the sensor wil be working as a digital device, and with some light shielding, will be somewhat insensitive to other light sources.

If visible light proves too noisy, use an IR emitter and sensor, with visible light blocking.

The parts should be under $2, so having two attempts shouldn't be to costly.