Hey Stevetgn,
About the dynamic IP address:
go to
www.dyndns.org and register some name for it, then that name will allways point to your current IP address. You will need to run the dyndns.org update client on your computer, but I don't think that will be a problem to you.
About the Router:
You will need to find an option in your router for a virtual server or something like that. This means that the public port your servers runs on, is routed to your own pc. Check your router manual for things like 'port forwarding' and 'virtual servers'. You are *not* interested in a DeMilitarized Zone / DMZ, as this poses a possiblesecurity risk.
About the Server:
An FTP server is probably the best if you want to have user accounts for a couple of people and if you need to upload stuff TO the FTP server. If the only thing you want is that the files on the server can be DOWNLOADED from everywhere, a HTTP server is probably way easier. I don't know of a way to limit permissions on a per-folder basis with FTP, and if there IS one, it's probably more complicated than that it is with HTTP. As a webserver I suggest the Apache Webserver which can be found here:
http://httpd.apache.org, but it will probably come with your distribution.
For the permission per folder problem look into a thing named '.htaccess'
For the folder indexes be sure to use: Options +Indexes.
I hope this helps you out, if you need any more help configuring the mentioned software, feel free to ask.
Greets, Target