If you can run OS-X, then you can get a copy of JDK1.3 for mac. However, it you can't run OS-X, you will be stuck with JDK version 1.1.8, unfortunately (although you can run Swing apps by including a separate jar file of the swing classes).
A great place to start is:
http://java.sun.com/docs/books/tutorial/getStarted/cupojava/mac.html
- a very easy-to-read checklist and resources, and a tutorial about how to get started on the Mac
Welcome!