For paid solutions, I've read good things about Expression Engine. There are a few EE pro's who frequent the CMS section so one of them might pipe in with some more info. On the OSS side (Open Source), I would go for the top and get Drupal. It's got a learning curve but it's hands down the most flexible CMS I've seen or used.
Now as far as your requirements go, I won't just shout out my favorite CMS and leave it at that without providing some follow up with regard to what you're trying to achieve...
1) If you're talking about User Profile data and functionality, Drupal is the unequivocal KING of users and profiles.
* I don't even know if that statement makes grammatical sense but is sounded good in my head :lol:
Seriously though, Drupal's user management is probably second to none and you can enhance the heck out of it. I see no reason why you wouldn't use the latest version (Drupal 7). In Drupal 7 you have typical user profile info username/password, signatures and pictures. You can add as many custom fields as you like through the admin section (yoursite/admin/config/people/accounts/fields) but if you really want to extend and hotrod your profiles I would recommend looking at the Profile 2 module. You can also integrate the GMap and locations modules with user profiles.
- I've built several sites that use Gmap and location user enhancements so that you can have filterable lists with addresses and locations of specific user roles.
** Oh for migrating users, you'll want to look at the Feeds module. There is another User Import module for past versions of Drupal but I don't think it's been ported to version 7 yet.
2) A multi-user/login feature with submissions subject to Admin management: This is an out of the box feature with Drupal. You can fine tune how it allows users to sign up in the user accounts admin section (yoursite/admin/config/people/accounts). It should be set up be default to allow anyone to sign up but an administrator must approve of the account before they can sign in.
3) & 4) will take some R&D to make sure you have a clean migration. There are lots of migration modules into Drupal. [Feeds again might be the best one to look at. Also look at the [URL="http://drupal.org/project/menu_import"]Menu Import](http://drupal.org/project/feeds) module if you just want to scaffold a site.
Ok, that should give you some direction.
PS: Any full featured CMS is going to be a resource hog with thousands of nodes of content.... If you're using Drupal you can try out the dev port of Boost. I've used it on Drupal 6 and it's pretty effective. There are optimizing and caching settings within the Admin Performance section of Drupal (yoursite/admin/config/development/performance) but there are many other ways to make the site perform. Here are a couple of discussions on that subject: