Correct seat height is essential to prevent contraction of hands. For more details on this, see Hand Position
Swivel is nice, for ease in reaching notes on far right and far left.
Metal stools do not match or look as nice as the old style wood piano stool.
But I now believe that metal stools are better,
because wood stools tend to squat and collapse.
I would say that the most important thing is to not fall. In my studio, two students have fallen from collapsing old wood stools.