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Install Eclipse IDE for Java EE Developers. This flavour of Eclipse is bundled with everything to start building Java EE applications. Download the Latest Release (Eclipse Helios) here.
I think Eclipse has different flavors, so pick the one that works for you. Java EE includes the servlet/JSP piece you need. I'd go with that.
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