The SE Runtime means that you're running Java Standard Edition, rather than Enterprise Edition (AKA Servlets/JSP, which need an application server). You should be just fine with what you have installed right now! If you want to develop Java programs, just make sure that javac is installed on your system.
EDIT
Also, make sure that javac is being provided by java-6-sun, otherwise you'll probably be using the GNU Java compiler which doesn't seem to be what you want.
You have to edit your eclipse.ini file and have to specify your jvm path at there. Read this link http://wiki.eclipse.org/Eclipse.ini. It will help you.
Best Answer
From a terminal, Confirm if the package is installed using.
List all the files installed by the package using
The listing of all files will help you to locate where directories/files installed by Ubuntu.