Part of the confusion about shinigami reincarnating is that is was explained in the manga, but omitted from the anime for some reason. http://www.onemanga.com/Bleach/46/03/
That page and the next explain it. I'm not sure how accurate the translation is, but what basically happens is that you are born as a living human in the real world. Once you die you become a plus. As a plus you either go on to Soul Society, Hell or become a Hollow. When a Hollow kills another Hollow, it consumes it and absorbs it's soul, increasing it's own strength. When a Hollow is destroyed by a shinigami it is purified and becomes a plus, and moves on to Soul Society. When a spirit in Soul Society dies, it's body disintegrates, becomes the spirit particles that make up the Soul Society and then the person if reborn in the living world as a new person. This does make sense, we already know that a soul has it's own constituent parts (such as the soul sleep, the soul equivalent of a heart and the seat of all spiritual power)
Apparently people can be "born" in the SS as well. I'm guessing that these are either the results of stillborn births in the real world, the fate of souls which are condemned to hell or the result of some still unmentioned other factor.