There is not, to my knowledge, a really commonly-used workflow that starts at Word and ends at typesetting. This is something Pandoc purports to do, but I would expect to lose most of your manual formatting tweaks from Word in the process.

Pandoc is a good tool for automating workflows that start with some other format and end with LaTeX.

Another good option if you like Emacs is org-mode, which has a LaTeX export, among other things.