Well, there are songs which need more than three chords, obviously, even some folk songs. But by and large most of the songs people are likely to know or want to know can be managed pretty well with just three - and they aren't necessarily any better for putting in more than that, to my ears anyway.

The implication of that is, just pick the songs because they are the ones the people learning know or want to know, and they'll almost certainly be three-chorders.