NEWBIE: Is CiviCRM RIGHT FOR US
It's an excellent choice for you. I've run Civi on both WordPress and Joomla and it does everything you are asking and more. Right now, I have at least a half dozen sites under my care on both Joomla and Wordpress. Depending on the size of your organization, Joomla may be the perfect, especially if the client is already accustomed to using Joomla. The ACL will probably be a little more familiar than in a WordPress environment.