You can have all 3 options as far as I know.

1. You can buy a hosting service which you can use to store your files in. This would usually cost you but the security and privacy of your files are kept. I am using a hosting which costs me $97 a year for 200G and they are having a promo of $22.40 for the first year. (message me in case you want this). With the hosting, you can upload files anytime and set passwords for authentication and usually accessible via browser or FTP client.

2. You can use free uploading based websites such as rapidshare.com or megaupload.com to store your files. The only downside is that the lifespan of the files are limited unless you pay for their services which is more costly than buying a host.

3. If you have a static IP address over your ISP connection, you can setup an apache or install the IIS server on windows to activate a web based hosting server via your own PC.