Recommended modules
Here is what I consider as the "shortlist" for such modules (quotes are from their project pages):
Special case: Organic Groups, which provides 'Groups' for Drupal users, and management of Access Control based on these groups. A great resource for learning about Organic Groups is the (free) video training about Learn Organic groups, a set of 14 videos.
My "recommended" module is Content Access ... Also because of al sorts of integrations with the Rules module.
For more details, refer to Access Control modules.
Rebuilding permissions
About "Rebuild permissions": any time the "Access" rules are changed (via admin settings), Drupal needs to ensure that these rules are applied to all impacted content (nodes). That's why Drupal then re-applies the updated access rules. A special case is the "installation" (actually "enable") of a module, when rebuilding permissions is also required. Makes sense? Clear enough?