I am creating use cases for a project. A generic user is extended by user "categories" which then is extended by an administrator (that can do all tasks possible).
Is the following acceptable to portray? Is there a better way to portray such info?
Yes. This is acceptable.
Making all actors a subclass of "User" is needless. That goes without saying.
The original Objectory method (on which UML is based) explicitly makes the case that "Actor" is a kind of classifier, and has subclasses and superclasses.
Don't go crazy however. The inheritance among users should be kept quite simple.
To me, it looks like you're drawing a Class Diagram, but with fancy stick figures instead of boxes. IMO Use Case Diagrams should show how a person or other entity acts or reacts under certain conditions. I fail to see how extending a client is something an administrator does as part of his job, or something an administrator object could be capable of.