Interesting quantitative take studying chord distribution. The basic takeaway seems to be that if you re-phrase a song into a different key you can play a lot with just a few chords (I IV V), and even more with a few others. While I would agree that you'll be okay playing any major scale in C major (or whatever other major key choose to learn), playing a song in a minor scale on a major scale just doesn't sound quite…
The chords in the key of C major will be the same chords in the key of A minor, although their patterns might be different.