Java 1.6 on Mac OS X 10.5?
Grumble. There are multiple versions of Java that can coexist on Mac OSX, and you have to run Java Preferences (in /Applications/Utilities) to select the default version.
I love my iMac but sometimes Apple just doesn't bother explaining some really simple stuff that would make life a lot easier.
So now I am running 1.6.0_15 successfully.
For checking if you have a 32-bit or 64-bit Intel Mac, see Apples thorough KB article.
For updating Java, have you tried software update yet? You can also download Java SE 6 from Apple.