Adobe InDesign is a complex and professional publishing application. It will easily produce artwork for the kind of book you are describing, including placing your Word files and illustrations. (I understand Finale will export musical notation as JPGs.)
You have to decide whether you want to invest the time in learning this program, and subsequently dealing with printers etc, or whether you should approach a local graphic designer and get them to do the design and artwork for you.
You also have the option with InDesign to produce eBook versions, including PDF, ePub, .mobi (for Kindle) and Adobe DPS. This book gives a good survey of the various formats: http://www.amazon.com/ePublishing-InDesign-CS6-publications-smartphones/dp/1118305590/ref= sr_1_12?s=books&ie=UTF8&qid=1371454183&sr=1-12&keywords=indesign
If you do decide to learn InDesign you can get help on this forum with specific questions. You will also (my view) need to undertake training preferably personal training in a small group or alternatively an online course such as those run by Lynda.com - http://www.lynda.com/InDesign-tutorials/InDesign-CS6-Essential-Training/96305-2.html
What Derek said. But I think all recent versions of Finale are able to
export postscript, and I think the latest version also exports directly
to PDF. So it would be best to use one of those, to keep your output
vector and maintain Finale's high quality.
Alternatively, if you have Acrobat you should be able to print directly
The point is to keep Finale's output vector when placing in InDesign.
The other Lynda.com InDesign training I meant to mention is (this is description is from their blurb):
Explore book design with Nigel French, as he breaks down the components of an elegant and readable layout and jumps into the setup and strategy for designing a book from the ground up in Adobe InDesign. This class covers document setup, placing and styling text, working with images, creating the book cover, preparing the book for print and or distribution as an ebook.
(I have no connection with Lynda.com)
InDesign is too complex and intimidating for any average newcomer, so you better turn around right now, UNLESS you're smart enough to create, compose, and annotate music, and write a book that teaches it.
In addition to the good suggestions already in this thread, search Google for terms like "InDesign books tutorial," "InDesign table of contents tutorial," "InDesign place import files tutorial," without quotes.
As in music, correct nomenclature and terminology help you find what you need. In InDesign (and many graphics and layout programs,) "place" means "import a file," using the File > Place command.