Collaboration Of Active Document-Client and I work simultaneously

I would do all of the primary writing and development in Word. It's a better tool for writing and editing, and sharing files is a bit less complicated. Even better, since you want to share more or less continually, use Google Docs.

When the text and structure is more or less complete, move it to InDesign.

I work things both ways, but tend to "write" in ID only when it's a solo project and I can manage both content and design/layout without any collaboration (==interference. 🙂 ).

InCopy is not a bad solution but it's a clumsy 'word processor' whose only real advantage is that it dovetails with an InDesign layout, which is of great value to magazine editors and the like but pretty meh for general collaboration.

You can't work on the same file at the same time - so like @BobLevine mentioned - communication is critical.

The way you share your document - is up to you. 

And using InCopy would be the best option - for text. 

Throw it all in a shared Dropbox or OneDrive folder but be aware that InDesign lock files do not sync so you must communicate to avoid any conflicts. If this is just about text, then I would suggest using InCopy.