"minimum" should handle the given width and height as max values meaning they are somehow a box into which the output file should fit. So since aspect ratio is maintained either you don't use the height fully or the width. For a fixed height I use to set width to 9999.
With "maximum" the output file will be at least width x height. So the the width x height box fits into the output box.
Hope that's somehow comprehensible.
That's at least what the docs say. I had strange results sometimes behaving like maximum when setting minimum, but that might have been side effects of other errors. When setting nothing it seems to use minimum.