Cable wires, unlike hard wires, are flexible and perfect for stringing bracelets and necklaces.    Cable wires are wires braided together and encased in nylon.  If the nylon sheathing is violated in any way, and the wires get exposed to the air, the wires immediately untwist and break.  In virtually all brands of cable wires, the nylon sheathing is very thin or porous.    This is bad.     Soft Flex brand, I feel, has the highest quality, thus the least worry for you about breaking.     

I recommend .018/.019" diameters for bracelets.    The major design issue for bracelets is how durable they are.    Bracelets take a beating.   You want the size that is both durable and still feels comfortable to wear.