I'm not sure zoo is your best choice here: as of last year it was lacking most access control configuration, which I had to manually add (at the risk of it breaking with a new release).
But from your description you seem to need a ticketing system / Q&A, may I suggest https://www.akeebabackup.com/products/ats.html Akeeba Ticket System, its solid, extensive functionality includes complete integration with Joomla Groups and an extensive guide on setting them up.
Community Builder doesn't include a Q&A so you would be adding a huge component and still need to resort to hacks and code changes to integrate it with zoo.
---- edit ---- Ok so you're back to adding ACLs support to Zoo. Still no CB is necessary. You might want to try aclmanager.
Also see here http://www.yootheme.com/support/question/11472 for a more complete reference (and rants about the missing ACL features, and a direct tip to achieve it without the aclmanager: http://www.aclmanager.net/blog/general/31-how-to-add-basic-acl-support-to-your-extension)