I have engaged in this question before, but now I am technically working out the legal implications of this with my thesis and my monograph publisher (Walter de Gruyter). Is it a problem to publish parts of your thesis as journal articles, and then to try and get it published as a monograph?
I cannot speak for all people and all publishers, but I have not found there to be any real drawbacks to NOT trying to get things published, in parts, as journal articles. Typically, articles are reviewed with more care and scrutiny, so it will strengthen your overall work as well. As for “rights,” there seems to be no real problem here either, as long as you have done your work to clear it with the involved parties.
If other have had negative experiences, like a book publisher expressing serious concern working with pre-published material, please do share that with us.
So far, it has been fine working with WdG. My only concern is that my editor is in Germany and it is not easy for me to just pick up the phone and call him, so a lot is done over email. While this can be convenient, there are lots of very technical questions I have had and corresponding about them via email can be challenging. Otherwise, it has been no problem.