I'm not sure a natural ordering really exists for a geometry, given that it is two-dimensional and can start from any point in its outer linear ring. However, to answer the second part of your question, the following will order by the left-most x coordinate of every geometry.
Select * from island_table order by ST_XMin(ST_Envelope(geom));
EDIT: As pointed out by MikeT, the call to ST_Envelope is superfluous, as the bounding box is available anyway to any indexed geometry, so it is sufficient just to write:
Select * from island_table order by ST_XMin(geom);
ST_Envelope gives you the bounding box, from where you can access the minimum and maximum values of x and y, using ST_XMin, ST_YMin, ST_XMax, etc.
I just did a quick test on some test polygons and if you sort by the WKT representation of a geometry,
Select * from island_table order by ST_AsText(geom);
you get something like,
POLYGON((100.00,.....
POLYGON((101.86,.....
POLYGON((102.17,.....
POLYGON((11.82,.....
that is in text search order.
Whereas if you search by the geometry itself, that is,
Select st_astext(geom) from island_table order by geom;
it sorts by actual values of the first x coordinate in the geometry, eg,
POLYGON((11.82,.....
POLYGON((100.00,.....
POLYGON((101.86,.....
POLYGON((102.17,.....
Neither of these are guaranteed to give you the left-most x coordinate, as the start point is not guaranteed to be left mest, so you are better off using order by ST_XMin(ST_Envelope(geom))