Most people think of the shutter speed first.
Sirius' point reflects the prevailing wisdom during the 1970s and early 1980s, when so many people shot relatively slow slide film.
That was one of the reasons that the Canon AE-1 was as successful as it was - unlike most competitors, it offered shutter priority automation.
In more recent years I would say that many more people who understand the difference tend toward aperture priority automatic systems because, providing that the shutter speed is sufficient, the aperture choice is one that has greater effect on the appearance of the photograph.
Most modern cameras that offer automation offer both and, from what I've observed, younger people are more likely to choose aperture priority. Younger people who seek to teach photography also tend to recommend it.
In the 1970s with manual metering I would choose the shutter speed first. Nearly a half century later I tend to do it the other way.
Old dogs you know ....
I first was puzzled by this comment by Matt.
But it may be that with people having started with film there is the reasoned fear of having not enough film sensitivity at hand, whereas with people coming from modern digital cameras this fear does not exist and that this may have an effect on choosing resp. looking at shuttter- versus aperture-priority.
My first SLR was a AE-1...