The series order is:
The Ship Who Sang (1969) (short story collection with stories from 1961, 1966, and 1969) ISBN 0-345-33431-0
PartnerShip (1992) with Margaret Ball, ISBN 0-671-72109-7
The Ship Who Searched (1992) with Mercedes Lackey, ISBN 0-671-72129-1
The City Who Fought (1993) with S.M. Stirling, ISBN 0-671-87599-X
The Ship Who Won (1994) with Jody Lynn Nye, ISBN 0-671-87657-0
This series also includes solo entries by Stirling and Nye:
The Ship Errant (1996) by Jody Lynn Nye, ISBN 0-671-87854-9
The Ship Avenged (1997) by S.M. Stirling, ISBN 0-671-87861-1
Omnibus versions of the above novels:
Brain Ships (2003) (includes The Ship Who Searched and Partnership) ISBN 0-7434-7166-0
The Ship who Saved the Worlds (2003) (includes The Ship Who Won and The Ship Errant) ISBN 0-7434-7171-7
The City and the Ship (2004) (includes The City Who Fought and The Ship Avenged) ISBN 0-7434-7189-X
You can buy all three omnibus editions from the Baen link above and get most of the books.
But the first, The Ship Who Sang, is inexplicably not available. There's a copy from the Virginia M. Woolf Foundation in PDF only:
http://ebooks.ebookmall.com/ebook/278117-ebook.htm
Also missing are two short stories, "The Ship Who Returned" and "Honeymoon"