What is correct representation of homogenous coordinates?

Solution 1:

Different people may write projective coordinates as $(x,y,z)$, $(x:y:z)$, $[x,y,z]$, or even $[x:y:z]$. All have the same meaning, as long as the context makes it clear that those are indeed projective coordinates (the first option may be confused by affine coordinates, but the space where those coordinates live is usually clear from the context).

I understand that you wished another answer, but it just doesn't exist. There's no "best" notation or "universally accepted" notation. As long as everyone understands what is being said, which is very often the case, all is fine.