I am trying to rotate my plane so that it is perfectly upright.
However I don't see this parameter:
Am I blind or are the rotation parameters hidden somewhere?
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This is because you are in Edit mode (↹ Tab). Try adding the plane in object mode to make it a separate object with it's own transforms.
That said, it's still possible to rotate geometry that's part of an object.
When you initially add the plane in edit mode there is an option to change its orientation in the Redo panel (F6):
And you can always use R to rotate geometry, e.g. RY
90 will rotate the selection 90° around the Y axis. See Why can't I translate parts of my mesh with the 3d widget?