If you set up the DS1511+ with a static address then it has a feature that walks you through setting this up and does all the hard stuff for you, including getting set up for dynamic DNS, setting up port forwarding on your router, etc.
That's probably what I would recommend since by your own admission you have very limited network experience.
If you are interested in setting it up manually I can walk you through doing that. Mine is set up so that I can access the console from anywhere on the internet as well as doing the upload/download file thing also from anywhere.
One thing you will need to do though if you want to do this is set up a dynamic DNS account so that you can get over the internet regardless of what IP your internet service provider sets up for you.