For my home internet setup I have a adsl router. The adsl side of the router has a public ip address and the local side has it's own ip address. The router takes care of the address translation to and fro. In the instance where you have a number of devices, the problem comes to access them publically - this is because the router can map a port number to a local ip address, but if all our devices use the same port number ( but different ip addresses ) we can't map the port to a number of local addresses. So, we need some means of 'aggregating' the local devices and combining this into one port that can be mapped to the outside world. You might also want to have a web page that allows you to check the status and issue commands to the local devices. For this you need a computer that runs a program written by yourself that connects to, or is connected to by your local devices via a tcp or udp port. This program combines (or aggregates) the data to and fro to another single tcp or udp socket. This socket is mapped to the outside world by the router. Therefore outside devices will connect to the nominated port at your public ip address. Your public ip address is given to you by your ISP. Now, if you wanted a web page, you need a program that will connect to your magic combiner program, grap the data it wants, process it and form a web page that can be published by your webserver usually running on the same local computer that the magic combiner program is running on. For the local computer, you have a number of choices. For me, I'd use something like a Linksys NSLU2 box which runs Linux and write a magic combiner program. These boxes also have Samba and a webserver running on them out of the box, so that leaves you to write a webpage and the various scripts needed to publish your data. You could also look at a hacked WRT54GL wireless router, again, running Linux. Or just a dedicated PC running Windows and a magic combiner program written in VB or the language of your choice.

I can tell you it is a big learning curve - I'm in the middle of it at the moment. But you must understand the basic terms - you seem to fling around the terms willy nilly without really understanding what they refer to. You need to understand the difference between TCP and UDP sockets, the basics of routing and the basics of the web page. Take a logical approach and it all starts to make sense.

Once you've got the basics under you belt, then you need to look at security.