If the ring is a solitaire, then I would say the long side parallel to the fingerlength, that would be a classic. The opposite is striking, unexpected, new. The first case makes your finger look thinner and longer usually.
In case it is set with other diamonds or gems, we need to see the ring of course.

In any case, enjoy your gems !

i like to see some of the band. it also give you the opportunity to have more diamonds. live a pave set down the band for more sparkle

I’ve always seen cushion cut diamonds set so that the long edge is perpendicular to the band of the ring. This will look better, especially if you have long or thin fingers. However, a parallel setting would be more unique.

It depends on how big the diamond is. I very rarely like it going horizontally. Vertically makes the diamond look bigger and allows for more decoration on the side. Personally I always like to see a little of the band.