There is not just one IDE
First, there are other good IDE options for Java development, with the best-known NetBeans and IntelliJ . But do not be afraid of Eclipse.
Proper Eclipse version for Java EE
To develop in Java EE, my suggestion is to go to the Eclipse downloads page and download the Eclipse IDE for Java EE Developers . This is just a shortcut to having Eclipse Standard + JDT (Java development tools).
Eclipse works with multiple perspectives
Although you have recommended "Eclipse Java EE", this does not mean that this version only allows you to create Java EE applications. Eclipse is an IDE that works with plugins.
A single installation can contain several of them and you can easily switch between different "environments" of development through so-called "perspectives."
Accessing the "JavaEE" perspective, Eclipse will show the panels commonly used for JavaEE development.
On the other hand, you could also install the Pydev plugin and switch to their perspective to develop in Python.
Finally, it is not necessary to have more than one installation. Just do not overload Eclipse with too many plugins as it may start to slow down.
Java SE and Java EE
In practice, there is no difference between developing for Java EE or Java SE. You will always create Java classes.
What changes are the APIs used, that is, interfaces that you use to implement a program or ancillary classes.
The biggest difference is that Java EE usually requires additional dependencies that do not come with the JDK but are available through an Application Server such as JBoss or Glassfish.
Application Servers
Note that Tomcat is not a complete JEE server, as it does not natively provide APIs such as JTA, EJB, JPA, JSF, etc.
Because of this, it is known as a Web Container , that is, a Web Application Server that only provides web-specific APIs such as JSPs and Servlets.
However, you can manually add third-party libraries to enable JEE APIs in Tomcat.
Additional Help
If you have questions about the basic installation and use of Eclipse Kepler, take a look at my article: