Hi Adam,
The shared files feature only allows upload by users with edit permissions on the page or module, other users who can only view the page or module can only download. Shared files is what I would use, of course its possible to use the links module or even the html module to link to files. Using file manage you can create folders beneath /Data/Sites/[SiteID]/ and you could organise files there as you wish, the urls would be http://yoursiteroot/Data/Sites/[SiteID]/[whatverfolderyoumake]/whateverthefilenameis.fileextension.
Hope it helps,
Joe