My 'dynamic' IP has changed two times in the last four years. One of those was when they replaced our cable modem, and the most recent (Feb or Mar I think) was when
Cox@Home (not a valid link, UBB just thinks it is

) switched over to Cox.net (ATTBI). The reason it is listed as dynamic is so they reserve the right to change it if they need to.
The way my broadband provider gets around users hosting their own stuff is by blocking incoming to port 80, as near as I can tell. Outside people cannot access my site (using IP only, my stuff is for a select group of people

) if it is on port 80. I ended up having the server listen on port 6669 (IRC) and it works fine.
Your provide could very well behave differently though.