The Servlet API is not part of Standard Edition
Java. And if you are just interested in Servlets and
JSP rather than all the other myriad EE technologies, you can just download a servlet container such as
Tomcat and it will provide the necessary jar files. That will be a lot less confusing than
all of JEE.
If you want to get into EJBs or other EE technologies (probably not, at this point), then you'll need JEE.