I have written quite a few staff handbooks.
Don't over think it.
Bear in mind that it is likely that someone else will need to maintain the document - so use a tool that is not only available to everyone, but familiar.
Clarity of wording is more important than lovely prose. If you use a particular phrase or compound noun, use that throughout (yes, this does mean that the language will be 'dry', but, clarity before elegance).
Most staff handbooks are referenced by people who have just joined, so make sure it covers all the stuff they need to know. 'How to find information' is important.
Honestly, unless your handbook is massive (hundreds and hundreds of pages), you can use Word for this. The outline and navigation panes allow for easy rearranging of contents.