After getting a grip on major, minor, dominant and half diminished chords, I think it's important to study fully diminished 7th chords and augmented triads, as they function harmonically in all 12 ...
Just as the augmented chord can be repeated every two or four frets on a guitar because of its note makeup (stacked major 3rds), so the diminished can be repeated every three frets since it is made up ...