The place where you registered your domain typically holds some entries for the name servers for the domain. Those entries have both names and IP addresses associated with them. So if you registered your domain name with Network Solutions, you can log in there and change the Name Servers.
Hardware specs are low, if all it's doing is handling DNS. An old workstation could be given a new powersupply and made to serve as your DNS server.
A static IP address should be on your priority list. Typically you can just ask your service provider for one and pay between $5 and $20 more per month for it.
I would have the MintDNS server's public name not be part of the domain that it's hosting, so that it doesn't have to be available to tell people about how to find itself. So if you have a couple of domain names, use one for your normal SBS network and give your DNS server a name in that domain. Then let your DNS server host a separate domain/zone for your dynamic clients to use.
You probably don't need an extra ADSL line, since the sort of traffic that this setup will generate won't be very high at all. Each time the server processes a renewal, I would guess there'd be less than 15k of back and forth traffic, and renewals won't even happen that often per client. You'll be able to monitor that and make a decision later if that's not true.
ShackDaddy
Shackelford Consulting