Mark, make sure that at least you know what classes are available in the java.lang, java.util and java.io packages. In particular, you should get plenty of practice using streams and collections.
Other packages and classes will come up as you need them. Usually when you're working on a project and you stumble into a problem that you don't know how to solve, you can search the web and it will often provide names of classes you can use.
I think it helps to narrow down your focus to a subset when first learning Java.
The specific classes and areas of interest for the SCJP / OCJP exam objectives seem like a good place to start. The exam includes some essential I/O, Collections, utilities, Exceptions, and of course, the wrapper classes. ( I might have missed a few, but you get the idea. ) An SCJP preparation book can also help guide you with a little more detail, once you get an understanding of the basic language syntax.
subject: What's the best way to get familiar with available classes?