Hi there, Stephen!
I work as a Java consultant in Stockholm. My primary areas are JSP/Servlets and Beans. The market here in Sweden might be slightly different to yours, but the areas which you are describing;
Servlets,JSP,RMI and EJB, are of great demand here as well as in most of the world I would expect.
My advice is for you to first get a thorough understanding of JSP and Servlets. The books I would recommend are 'Core Servlets and JavaServer Pages' (isbn: 0130893404) and 'Web Development with JavaServer Pages' (isbn: 1884777996).
Now you might first want to implement your new knowledge in some interesting project, why not build your own web site!
When you feel you are hungry for some more interesting and challenging information, you could start getting into EJB's. A good book for this purpose is 'Enterprise JavaBeans, 2nd Edition' (isbn: 1565928695).
I hope this will be helpful for you, happy hacking!
Regards
------------------
Dominic Steng�rd
Sun Certified Java 2 Programmer
------------------