The way I started, and the way many people start is to memorise each chord position in the twelve keys by going around the key circle. For example take the major chord plus octave C,E,G,C and learn it in all keys by playing it around the key circle in C,F,Bb,Eb,Ab,Db,Gb,B,E,A,D,G. Then do the same thing with the other two inversions (E,G,C,E), (G,C,E,G) then the minor chords, then any other chords you want to learn.
I don't know what styles you want to play, but if you want to play tunes in, say ,stride or swing, then use the same procedure with left hand basses. The method can be applied to whatever way you want to play your chords. The object is to become so familiar with all common chord types in all twelve keys to the point where the response is automatic.
If you just intend playing single note melodies in the right hand accompanied by simple chords in the left, then just do this procedure for whatever chords you intend using, maybe just left hand triads.
Practising the chords in this way won't predispose to favouring particular keys and after a while you should be able to play any given chord instantly without having to work out its position.
If you can visualise the keyboard you'll find that much of this sort of practice and chord learning can be done mentally away from the piano.
