Controlling READ Access to page and/or topics

WordPress seems to be near perfect for an application I am working on,
however I need a way to restrict READ access to various categories/topics
to only certain registered users. I would envision operation where a new
user (or general public) would only have LIMITED read access. Later, an
admin could grant READ (and post) access to other categories/topics. I
have been looking through the docs but don’t see anything covering this.
Is it possible? Is there some other tool that would be more suitable for
this kind of operation? Thanks.