Your plan looks good but can be better. It really depends of 1) how much time you plan to learn for each topic and 2) how deep you want to go. Also I'm assuming web design you meant CSS stuff and not graphics.
JEE also has JSF, EJB, persistence (JPA), web service, messaging (JMS) to name a few. Furthermore, beyond the technologies provided by the Java EE platform there are open source frameworks and tools like Spring, Struts, Ant, Maven, Hibernate etc. The list practically goes on and on.
But first thing first. Core java and OO concepts are must be the first step. Here is what I suggest:
1) core java + OOAD + start design patterns (eg GoF) + Ant and Maven build tools
3) JSF/JSTL/EL + even more design patterns
4) web service + EJB + JPA + rest of design patterns
5) open source stuff (Hibernate, Spring, Struts etc) what ever your interest
Practice is always a key in the learning process. I mentioned start learning design patterns right from the start especially the Gang of Four (GoF) patterns because it surely will help you in your OOAD and programming (one you know how to apply it that is). Design patterns topic is huge, there are like 23 GoF patterns then another set of "J2EE core patterns". Beyond these there are security patterns, SOA patterns, cloud patterns... depend on the scenario and scope.
I also recommend learning Ant and/or Maven build tools from the beginning. Rather than doing compiling/running through batch or shell scripts, Ant and Maven should enable you to do the same.
Thank you for taking out time to answer my question. Thank you so much for your detailed suggestion.
Yes I meant CSS stuff, you were accurate in your assumption.
I have started studying Core Java and I have bought the GoF book too. I had a different immature plan in mind, but now I'll follow your plan, I am feeling very happy after reading your reply.
Thanks again for your mentor-ship.
I didn't think of Ant and Maven previously and I had no idea about the break-up of design patterns.
I have thought of following the Head First books for all the topics and GoF for design patterns.