Small company (8 people) - SharePoint Online Teamsites, Groups or both?

Thanks all for your suggestions! Alltough Teams looks like an interesting solution (a friend of mine is using this approach in a kindergarten/daycare situation where he is part of the staff), I think this is to far out of the comfort zone for my own customer. Until now they have used Windows 7, Offfice 2010 and a SMB2003 server and file storage. The step to Windows 10, Office 2016 and Office365, SharePoint Online, etc. will be a big one. I even got a CEO who wants to save every (usefull) email in a folder structure :S 

My own idea is to go with a minimal set of Groups, one for each department. Hopefully I can convince them they can then use the OneNote Notebook for Meeting Notes etc., the Document library for files, and Planner to centrally manage things that need to be done.

Maybe I create a Document Center for central archiving, but that depends on the kind of files they have. I will know that tomorrow, when I have my next meeting.