J2SE SDK is the compiler. What you probably want is IDE (Integrated Development Environment) wherein you can write the program, compile it and test it and finally prepare it for distribution. Eclipse can be used for this, or you can try Sun One Studio... There are a couple of other good free IDEs available that you can reach by searching on
www.download.com - some are more bare, leading to a smaller download size but a slightly larger learning curve...
Thinking in Java is a great book for those who have decent knowledge but a really tough book to use for beginners... If you have knowledge of C++, go for TIJ... If not, try some other site such as *java.sun.com/docs/books/tutorial/ where I found a pretty good and easy to learn tutorial (available for download also)
Arun