Speed test between clients and server

nethogs will show you how much bandwidth each client is consuming - assuming you are on linux.

This looks like it might be similar for windows.

You best bet is to log this information at your firewall if you can. I know of a few firewalls (PFSense comes to mind) that will provide this information in a real-time graphical display (a breakdown of in/out speed per source/destination). It should be possible to log this information so that it can be parsed at a later date for analysis.

continuously downloading media files

...implies streaming

e.g. through apache

...but apache is not a streaming server.

But leaving that aside, what's wrong with the standard apache logging mechanisms? (for preference using %I/%D rather than %b/%T, although in both cases you'll get a better answer using regression).