Best thing would be start with something that would make you work on core
java concepts. Get a strong foundation on core java skills. J2EE will follow if you are interested in working on
JSP, EJB's and other J2EE related technologies, also you would get chance to work on frameworks like
Struts etc.
If you are fresher then IMHO your goal should be to focus on J2SE (core Java part). Even if you are working on J2EE then also automatically you will be working on core java + some other technologies. Try to use java docs and dig through the java API documentation.
Once your core java is good you can then master the other skills with better understanding. As of SWING it too is part of core java. I personally prefer J2EE.
Ya, you guessed right I am working on J2EE technologies.
J2EE exposes you to more technologies that is the advantage.
Also, I know that as a fresher one is not in position to choose what he wants to do! Usually things are decided on the job opportunities but if you ever get a choice to decide then IMHO your focus should be to get maximum exposure in initial 1-2 years. Period! Later things will take care of themselves I promise you!
Hope this helps.
BOTTOM LINE IS DO WHAT YOU LIKE TO DO!