New composite-coated flat-rolled steel product and new methods of manufacture in which low-carbon steel, as received in cold-reduced continuous strip form is prepared for plating, a corrosion-prevention plating is applied, and a selected polymeric coating with lubricant is applied as the finish surface. The resulting composite-coated steel substrate is cold-rolled to decrease the composite-coated steel substrate gage. Selection of cold rolling steps, with non-use or selected use of stress-relief type of heat treatment before and/or after an initial cold-rolling of the steel substrate as received prior to surface preparation, provides for selective tin mill manufacture of composite-coated steel of various weights per unit area, for example, in the range of about 35 to about 100 lb/bb, produced by cold rolling of the composite-coated flat-rolled steel.