While I have definite opinions on this subject, I fully acknowledge that there could be other writers that completely disagree with what I say. Because I know that this particular subject has no particular consensus, I will endeavour to explain why I have the opinions I do.
When learning about chords and how they are constructed, it must be understood that many chords are built the way they are because of the keys they are built from. I am not talking about piano keys here, but rather the keys that are reflected in various scales, in other words the tonality.
I think it is best to learn major chords first – specifically the ones that contain just three notes. The most obvious to start with would be C major, G major and F major. Once these were thoroughly understood and familiar, I would then recommend learning D major, A major and E major chords.
After this I would encourage learning minor chords, specifically how they are technically different from major chords. It would also be useful to not only understand how the minor chord are technically different from major chords but become really aware of how they sound different.
A minor, E minor and D minor would be the most logical minor chords to start with, not just because they are very common, but because they are the simplest minor chords. After these are learned, I would then recommend B minor, F minor and C minor.
Once you have learned these chords, then there would be many pieces of popular music that you would then have enough chords to play. In another blog I compiled a significant list of the sort of music that you could play with just these chords. Its important to note that my list wasn’t comprehensive at all, but rather an example of what music could be played with 4 simple chords. You can find that list here: http://pianoforretirees.com/do-popular-songs-really-only-contain-4-chords/
Due to the fact that the vast majority of our western music uses major keys or minor keys, then it makes sense to learn the chords that are taken directly from these keys, first.
Once you are very familiar with a number of major and minor chords, then I would recommend learning seventh chords: major sevenths, minor sevenths and especially dominant sevenths. I think these chords are essential to learn eventually as they often make the music have more depth of sound and add another level of interesting sounds.
After this , your knowledge of chords should be fairly comprehensive. As there is other chords such as diminished and augmented chords, I would encourage you to learn these as well. There are also some lesser known chord types that would expand your knowledge and potentially improve your piano playing further.
When it comes to learning chords, you can never know too many different chords and how they are constructed, but you can’t learn everything at once and you need time to learn and become familiar with each of them.