Why do you prefer a home-webserver, instead of using the now-abundant free file hosting services on the net? With the webserver, you'd need to keep the pc up all the time, and if you were to also use the same connection for your daily browsing/torrenting/gaming/whatever, anyone downloading from you would get very poor download speeds to boot. And i don't think a separate line for the server is cheaper than hosting services

If you're accepting alternatives, maybe you could try sharing through irc file servers? They have a more established community around this "from home" file serving with persistent queues, bandwidth caps and stuff. Or maybe try something with torrents?

As for filling the dedicated server storage, i think you could initially just copy files disk-to-disk by connecting the server disk to your own pc, and after that uploading through the net whatever new stuff comes out. And when you get some followers for your web site, you could ask them to upload stuff for you