Permit configuration of own A, CNAME, MX & TXT records, either directly, or at least by email request.
One time: Register with the ISNIC, including registering a zone contact and the nameservers.
Using Google Apps for now, but may require ability to use scripts to parse some inbound email in future.
Almost all outbound emails will be for the purpose of confirming new member accounts,
(i.e., to mitigate bad behavior), so need reasonable and flexible usage limits.
Ideally, separate IP address for each tertiary domain hostname, but unlikely, due to IPv4 shortage.
In lieu of that, permit own .htaccess for redirection.
PHP 4 or 5
If using Accountify:
GD graphics library, including Freetype text output
Configurable in some manner.
Web-based admin nice, but not absolutely required.
Administration (by host)
Regular backup of files and database.
Maintain system security.
In general, a "can do" attitude if I find I need another package installed, (within reason),
e.g., an additional PHP library along the lines of what's shown above.