Z-order in JavaFX is actually the order in the scenegraph, eg. in the content sequence of the scene (then in the contents of the groups, containers, etc.).
All nodes have also toFront() and toBack() functions to help changing this order. For finer control, you have to remove nodes from one place and insert it higher or lower in the sequence.
With the toFront() and toBack() functions you can indeed influence the z-order, but be aware that this also influences the layout. The HBox and VBox for instance also use the sequence of children to do the layout and moving something to the front will also move it to the end of the [HV]Box. This might not be what you are looking for.
I was looking for a way to do an animation with the animated Node on top of all others, without messing up the layout. There seems to be no way to do that because the z-order and layout order are both taken from the child-order.