Why not both? Make a custom domain for the book, then treat your own site as if you were guest-blogging on it to pump link juice to the custom domain.

That way, your venture ends up with the combined page-rank of your personal brand and the exact-domain bonus. (Whereas if you just redirect from one to the other, you lose one or the other.)

If you have a domain name already, use it. I launched with just a page on my blog and later moved it over to a separate domain. I don't think it matters in the long run, and in the short run you get a boost from your personal domain that people already know.