Well, the modt common choices that come to mind are Wordpress, Drupal and Movable Type.
Wordpress is a bit of a problem these days. The code merge of WP and WP Multi-User means you have WPMU capapility in all versions, but it no longer has support for separate root domains (only easily does subdomains and subdirs). There are tutorials out there about how to do it with root domains too.
Drupal has this built in for domains, subdomains, and subdirs. This works quite well out of the box, but requires the admin to do a few simple things on the server. You can set up the admin end to handle this using the Multisite Manager [drupal.org
...] (I've never used it).
The big caveat, is you should decided which modules and themes you'll make available to your users, and keep that number as small as possible. That will keep updates as infrequent as possible.
Updating multiple sites is a real hassle if you have a lot of them, but if you have complete access to the server (which obviously you do), there are tools to help
And then of course Movable Type was also built with this in mind
As for the static page generation, WP and Drupal have modules that create static pages and MT has this built in.