when to use NULL and when to NOT NULL DEFAULT ''

PG peeps:

What's the prevailing wisdom & best-practice advice about when to let
a varchar (or any) column be NULL, and when to make it NOT NULL
DEFAULT '' (or '0000-00-00' or whatever) - in PostgreSQL?

{Moving to PG from MySQL where we were always advised to use NOT NULL
to save a byte or something. But that was years ago so sorry for the
stupid-sounding question, but I had to ask.}