Creating multi layered / location Sharepoint sites

Hi,

We are looking into sharepoint 2013 as a way to create cloud based document libraries for 1 corp. office and 17 locations. We envision it as a top level Corp site with 17 team sites / site collections underneath and one public site where invited users can access docs from library. We would like to share docs across team sites. Each site would consist of library and news feed.

We have a basic idea of structure but would like a little layout guidance from the experts.

Thanks.