Since you have a budget you can select a CMS and post the requirements in first post on freelance sites such as rentacoder.com or elance.com and take bids from coders to taylor the CMS to your needs.

For this particular program it looks like Drupal is a better candidate than Joomla for following reasons according to comparison run on cmsmatrix.org

Drupal has granular privileges while Joomla has not, as explained on site granular privileges is that "the system allows read and write privileges on a per page or per content item basis, as well as separate privileges for other system functions". This is I believe important to grant the layered privileges needed for amount of personal information available, from very little to the anonymous surfer to everything including ability to kill account by administrator.

It also has public mailing list while Joomla has not.

Hope this helps, good luck.