From what i understand, the media files are yours and are on your server and the WinForms client will be used by your users to view the files and at the same time be updated on any changes on the files.
Now, let's suppose your users are located on your network at first. That leaves you with an open set of options and your main concern becomes performance and any security issues you may have with users modifying the files. On this scenario, i think the best will be to transfer them using mere IO through UNC files. But that will require you to modify permessions on the files to allow only reading of the files for the public. That should be relatively easy and secure over your network using NTFS and AD permissions infrastructure.
Now the next step will be assuming your users are all over the planet, with your files exposed merely through web technologies (FTP/TCP/HTTP ... etc) In this scenario, and if what i remember is correct, performance will be best through FTP then TCP then HTTP (in units of speed) becasue of the extra headers and sesions added by each protocol in the chain. However, a methodology that is gaining much popularity and praise is using Web services for your purpose. This will be through creating a web service that exposes methods to download the files and others to query update information. This will give you the following extras:
1. You're in control of the security mechanism, and you can use layered security levels (with NTFS at the bottom, Web Forms authentication above it and maybe any other security protocol above them all (session tickets, expiry policy .. etc.))
2. You can totally hide your files deep in your network as the web service is the users point of contact, the user will only have the address of the service and nothing more, no infomation on where your files are, what they are named ...etc.
3. You can later upgrade your security measures, enhance implementation of the webservice and change the files location and format with nearly no cost(if any at all) on the client side
4. You can notify the users of updates not only to the media files, but also to the client program itself and make it possible for them to update the client without requiring any experience in using computers.
5. You can support pausing/stoping/resuming download of media files on your client
However, this comes on the cost of performance. Web Services operate based on HTTP and that - many will argue - is slower than other protocols. I don't know about you but, for me, just the ability to give my users the feature of pausing/resuming their download can be enough.
In my opinion, this might just be your best option. BUT, that's just my opinion.
Hope this helped