You'll typically need to be familiar with the Java programming language, especially if you want to make use of some of the core API type features. The book currently has all examples in Java, however Neo4j run in server mode can be accessed by any client capable of talking to it via its HTTP REST API. Other than that, a willingness to learn and think a bit differently should suffice!
The book does indeed provide opinions and examples of where Neo4j would probably prove a better fit compared to, for example, a traditional RDBMS.
You can't have everything. Where would you put it?