The cross ratio relates the positions of four co-linear points in 3d space. I understand definitions a published online, such as that from wikipedia:
https://en.wikipedia.org/wiki/Cross-ratio
However, I'm am unsure what the general rule is for point selection in this ratio.
It's mostly a matter of convention. In my surroundings, one would define
$$CR(A,B;C,D):=\frac{[A,C][B,D]}{[A,D][B,C]}$$
which is the same order Wikipedia uses. I assume that convention to be the most common one. But I, too, have seen other conventions, so it's best to check what convention a given source is using.
I'd use $[A,C]$ to denote a determinant of $\mathbb{RP}^1$ homogeneous coordinates, but others use other symbols here, sometimes $AC$ for the (oriented!) length, sometimes $A-C$ as a difference of (non-homogeneous) coordinates. Mostly a matter of notation and convention, once you've seen that all these things are essentially the same.