We are finishing our basement and adding two bedrooms and a bathroom.
The basement right now is completely unfinished, with a concrete floor
and walls.  I am looking for information on finishing the basement
floor in the bathroom.  What kind of flooring is best for a basement
bathroom?  I would also appreciate advice on whether to use a
subfloor, how to keep the moisture from degrading the floor and walls,
and overall make the bathroom last a long time.  Thank you!

google "permacrete" and "concrete acid stain".  There are several
companies that install these concrete coatings.  They can be made to
look like tile and many other things.  Another flooring is terazzo
(?).  May be difficult finding someone who is skilled in installing it
though.