i went through almost exactly the same thing 2 months ago.
I replaced a polybutylene run from the basement to the kitchen sink
because of a pb leak in the basement.
anyway, i used cpvc pipe from the basement to under the kitchen
sink, used a special cpvc valve and connected the
usual steel mesh covered flexible hose from the cpvc valve
to the faucet connection. I also replaced the kitchen faucet at
the same time since it was a piece of junk.
anyway, the picture is almost exactly the same as this:
http://www.rd.com/images/tfhimport/2000/JA00_CPVC_Basics/20000701_CPVC_Basics_page008img001.jpg
except that my cpvc valve is a right angle valve.
my valve was all one piece (i suppose it could
be made of parts that are screwed together, but i never
tried to take it apart). home depot sold everything
i needed.