When I first read CORDELIA'S HONOR, I wanted to read A
CIVIL CAMPAIGN (just because I had heard it was very
romantic) but a friend who really enjoyed Bujold told me
that I would regret not reading the books in order. She
said that you really do not "get" the humor and the great
characterization if you are not already familiar with the
cast of characters and what has happened to them in the
previous books. After reading all of the books in order, I
realized that she was right -- A Civil Campaign was so much
better because I knew where each character was coming from
and why the way they were acting was so funny.
As much as I hate to say this (because it means that you
will not get to A Civil Campaign for awhile) I really
recommend that you read them in order -- I think that you
will get much more enjoyment out of the story.