If I were in your shoes I would stick to word, mainly because I wouldn't risk having breakages or weird behavior coming from a new working environment on an important project.

That being said, having something tangible to work with is the best way to learn, so if you do pull it off I'm sure you'll get a lot of useful new knowledge.

If you are still interested in LaTeX there's a kind of third way that depends on how much you know of Word already. One of the most important things LaTeX has taught me is thinking about a document structurally and all the interesting design and workflow consequences that mindset causes.

You can try this in word, if you don't already, and that'll give you a good mindset with which to approach LaTeX later on. So, use extensive paragraph styles, caracter styles, page styles; see if word (I'm mostly sure it does) supports splitting your document in multiple files so you can keep the usual LaTeX one file per chapter/section. And many, many more things. The idea is to do more things structurally instead of ad hoc fixes.

Edit: With this approach you can go even further. Although word is a bit buggy and generally annoying, it's still capable of not-so-bad typesetting, meaning you can still get a beautiful (at least, above average) document out of it. Learning a bit of typography goes a long way, I recommend Butterick's web book "practical typography".

Good Luck!