As one of the prerequisites for the ISP in a box documents for your Mac mini is having a fixed IP-address. This enables you to connect your domain name to your ip-address using DNS. There are some possibilities documented in using a dynamic ip address but I now found this article that explains how you can have a domain name attached to a dynamic ip-address without to much trouble. I don’t know how it will work as I have the luxury of a fixed ip address for my server. If someone with a dynamic ip address would let me know how this works out for them and if you can add MX records as well for use with a mail server.
As Urs noted in his comment, it is possible to use MX records (you need them to be able to receive e-mail) with www.dyndns.com.