For sake of efficiency I would think about going through a thrid Party like Dropbox or Amazon S3 for example because the Upload of your Internet might be really slow depending on your speed and file size, while those providers offer really good down bandwidth whereever you are.
If you really want to do it from home, you could setup a VPN and and keep on accessing your files via SMB over the VPN. Another Idea would be to setup Apache with WebDAV support, so you can map the drive via the Internet, make sure you use https (SSL/TLS) for access so to be safe. You could use a Provider like DynDNS to give you a static Domain via which you can acces your (maybe changing) Home IP.
All those approches are Cross Platform btw. Personally I have a Remote Server running Apache with WebDAV, and a Dropbox Account to share files between my Work, Home and Laptop. While I gotta say Dropbox is really the easy route.