This is my take on this:
Pickups emphasize certain frequencies and add some of their own characteristic to the overall acustic sound. After all, pickups don't generate any sound by themselves, they just transform the vibration of the guitar into an electric signal. Many players think of pickups as an extra EQ slapped on the sound of the guitar, but I think the "emphasis" idea I have is a better representation.
Typically from there you go with the pickup that builds on the strengths of the wood of the guitar, or which emphasises some frequencies more that you'd like to see in the mix and that are lacking at the moment. The characteristic is mostly important for styles, which is why different pickups are grouped with different styles quite often.
Lastly, the art is really in finding a pickup that matches well with the acoustic sound of the guitar, adjusted for style. The wood type is supposed to help with that, because it allows others to have a general impression of the acoustic tone of the guitar. However, more often than we'd all prefer, one piece of wood can sound quite different from another piece of wood, which is why, in the end, it has to be your EARS, not the general advice from people on the internet, that make the final decision. For example, I have three guitar with mahogany body and each of them sounds quite different.
