I tend to think of chords more along the lines of how the relate to the major scale.
So a major chord is the 1st 3rd and 5th degree of the major scale.
Minor is 1, b3, 5
Diminished is 1, b3, b5 and major 7th is 1, 3, 5, 7

There is nothing wrong with the way you are looking at it though. I learned that way as well, but have just come to prefer thinking about it the way I just described.