BIND is very complicated, and full of security holes. Stay away from it.
djbdns will do what you want with much less hassle. It is much easier to set up and maintain, and has never had any security holes (it's been around for over 6 years). Specifically, you want the tinydns component which deals with publishing DNS data.
Only other point to mention, you will need two DNS servers on separate IP addresses (this can be one machine with two IP's assigned to it). So your cable connection can be one of them, but you will need to either get secondary DNS from somewhere (some places offer it for free - check Google) or get a second IP address from your ISP.