Best way of implementing mp3 file upload/download site ?

I have been asked to develop a site for a group of choirs, with each choir wanting to be able to upload mp3 files of their performances into their own folder, (which is only accessible to members of that particular choir or the admin team above them), so here is the hierarchy...
Top level admin, upload to / download from any folder
Individual choir admin, upload to own folder only
Individual choir member, download from own folder only

Creating the admin and file manipulation isn't an issue, but as some files may be 10mb or so in size and am conscious that server timeout may be a potential problem, especially with shared hosting space.

Should I be thinking of using their web host - as I have experienced problems in the past with server timeouts, or am I better considering cloud storage (such as dropbox and their api )?

Previously, I have had issues with a site I created trying to send only a couple of hundred emails at once, and I had to go the mailchimp api route (which works well), but I don't want to develop something which works locally but fails on the host.

A second consideration is that their host does not allow files to be stored outside the root folder, so I may be compromising on file security.
If I password protect a folder (using htaccess?) within the site root, can I automatically provide the password within my php page so the web user does not see the protection ?

Grateful for any advice, experience