I didn't have a unique (permanent) IP address. Just a standard BT broadband with a dynamic IP . The domain name is registered with
www.dyndns.org, who also do the DNS service for it. On my Linux machine I run addns.pl every 20 mins, which updates the IP address held by dynDNS if required. This way if I have a power failure, the line drops, or whatever, the IP address corrects itself at the DNS with a max downtime of 20 mins. I think dynDNS, or addns.pl, complain if you try to do this more than once ever 10 mins. So to anwser your question Richard, zero cost.
Since I first started this thread increased traffic has persuaded me to move the site to a server with a much better permanent connection so I'm no longer using addns.pl for this particular site.
Regards
Stoney