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Execute this in your terminal:
sudo apt-get install eclipse
sudo apt-get install openjdk-6-jdk openjdk-6-source openjdk-6-demo openjdk-6-doc openjdk-6-jre-headless openjdk-6-jre-lib
The first one installs Eclipse (you will be asked to enter your password), and the second one installs all the Java stuff you may need!
Don't install Eclipse from the Linux repositories. These repositories may not be up-to-date with the last versions released by Eclipse. A better approach is to follow the instructions in this answer from Ask Ubuntu. For Java programming, make sure you have a JDK and a JRE installed
apt-get install openjdk-7-jdk openjdk-7-jre
You can download whatever Eclipse Java IDE version suits you best from the Eclipse website (link to the Eclipse v4.4 (Luna) release).
No, but you can update classic version for it to be same as Eclipse for J2EE version.
The best way (which I know) is:
1.In Eclipse go Help -> Install new Software...
2.Press Add...
3.In address enter http://download.eclipse.org/releases/indigo/ and name - whatever you like.
4.Install JavaEE Developer Tools (under "Web, XML, JavaEE, and OSGi Enterprise Tools")
5(Optional, but very useful).Install Marketplace Client (General Purpose Tools -> Marketplace Client).
That's about it, after this you should have the same environment as client you would download from Eclipse.org.
Eclipse comes with differents configurations but there is always the same "eclipse" as core application. They are the same Eclipse with differents collections of plugins that you can install, remove and update trough the package manager integrated in Eclipse itself. That's why you can't find the Eclipse you want with an apt package manager.
You also do not need to install eclipse or java ( the .bin version from the Oracle website ), they can be unpacked in a local folder, for example you can unpack this two in your home folder and then add the -vm option to the eclipse.ini or launch eclipse with the -vm option, example:
\local\path\to\eclipse -vm \local\path\to\the\java\machine\used_by_eclipse