Whether you should publish as many individual pieces of your book in separate places before the book itself is published is subject to some debate. Some presses prefer that the work in your book be all new, or as new and unpublished as possible. This way, the book has more to offer the reader.
DVICE. Publish everything you can, each individual piece, even as you are showing the book manuscript around. The idea that the contents should be unpublished work is not particularly in service to the writer--it is in service to the press. It is true that a book should offer to its reader as new a countenance in all things as possible. It is not likely, however, that even the most attentive reader will have read each of the individual pieces in all the places you will publish them.
"Nothing stinks like a pile of unpublished writing."
Once you find a publisher for your manuscript, and in the hope of establishing a long-term relationship, you will want to find a balance of how much unpublished versus published work to include that serves everyone. This is common sense. Before you find this publisher, however, send everything, all the time, and right back out when it comes in. When your name starts appearing places, people start remembering, and reacting. This would seem to help all around, and you most of all. In the beginning, helping yourself is imperative, as nobody else yet knows you. The prudence of putting all your eggs in the basket of a single full-book publication is something to think seriously about.
"So many, and so many, and such glee."
In a word, work everywhere you can keep doing work.