Hi,
As far as I know, photodiodes are faster than phototransistors. So if you are interested to obtain good response for fast signals, use a photodiode followed by an amplifier. Phototransistors are more sensitive, they are able to generate an electric signal from a weaker optical signal (because of the amplification of the transistor), but they operate better with slower signals. I consider 15kHz is not a very fast signal anyway, so I'd first give a try to a phototransistor.
You should drive your led between zero current to nominal current, this way the signal will be more easily recognised by photoelement. Of course, the highest sensitivity of the optical signal appears in darkness, ambient light will have a negative impact. Usually they use IR filters in front of the receiver, which block significantly the visible light, but let IR pass through. The phototransistor you indicated has IR filter, so that makes things easier. Also, fT is about 7 times higher than your signal, so you can use that phototransistor.
You should do some tests, you only need a few components for transmitter and receiver (could build the transimitter with a LM555 and the receiver with a photoreceiver and an opamp or two transistors for example and check the signal amplitude with an oscilloscope, if you have access to one).
Regards,
Nicolae