Regarding IDEs:

I have used "Borlands JBuilder 7", "Sun One Studio 4 EE & CE" and
"Oracle's JDeveloper 9i", my personal suggestion is Sun One Studio, but,
for projects related to Web Services I suggest using Oracle JDeveloper
9i.

There are some features that are excellent in SunOne Studio and some are
excellent in JDeveloper, its related to your project. Leave JBuilder.
(This is my personal suggestion, and could be wrong)

Regarding GUIs:

They will work  on windows platform  as well, however, if your project
used filesystem or things like that try to code in a way that is
acceptable to both OS. Ex: C:\Test is OK with windows but not with
Linux. However, C:/Test is acceptable to both.

Regarding Applets:

Applets execute inside browsers, older versions may cause problems but
not the OS. Say, If your applet  executes well inside Navigator and IE,
it should execute on Linux as well, (if the versions of Navigator and IE
are same)

Regarding Application Development:

For java  coders, these publishers are excellent

1. Deitel Associates - <http://www.deitel.com> http://www.deitel.com
2. Wrox Press - http://www.wrox.com
3. OReilly Series