Is there some kinda premade platform or plugin I can use to make a site people can upload files to and also display everything that's available for download?
I used this in the past, very simple http://www.maianscriptworld.co.uk/free-php-scripts/maian-uploader/free-file-upload-system/index.html
I'd defo go with making one yourself as Milo suggested Tai. Learning some PHP / Java can only be a good thing.
Get yourself on W3Schools or something & code away.
V true knowing php would be handy but got no motivation for it atm. Plus when I can knock something like this up in an hour it doesn't seem worth it lol
http://www.mirfiles.co.uk/index.php