With wordpress, your visitors can register for a membership to your blog. Go to Settings and look for Membership. Check it for "Anyone can register" All new registers would automatically be placed in the Subscriber group, the group whose members can only read the public and private posts in your blog. You can determine which one of your members can add posts or edit posts in your blog by promoting him/her to the Contributor, Author, or to the Editor position. For more info, see here:
http://codex.wordpress.org/Roles_and_CapabilitiesUnfortunately, the members of your forum would have to sign up again or register again with your blog. As far as I know, there is no bridge plugin that would integrate your phpbb or invision or whatever forum, with your blog. All I know is you can use
this instead for your forum. It integrates with wordpress. Even if one has a wordpress.com account, he/she still has to register with yours.
If you want your members of your blog to have a separate blog of their own, you can use MU Wordpress but I think there are some functions that you need to enable before you can install MU Wordpress in Zymic. I'm not sure. I can't remember ever trying to install that in Zymic.