[1] Johnson R. (October 2002). Expert One-on-One j2EE Design and Development (Programmer to Programmer). Indianapolis, IN: Wiley Publishing, Inc.
This book actually predates Java EE 5 and is more about the genesis of Spring (back in the J2EE 1.4 time, when things were hard). A good book to read at least once anyway, but not really about modern Java EE.
[2] Alur D., Malks D., & Crupi J. (May 2003). Core J2EE Patterns: Best Practices and Design Strategies (2nd Ed). USA: Prentice Hall
Again, this book predates Java EE 5 and is a (bloated) repository of patterns for J2EE 1.4. First of all, I consider it more as a technology showcase than a pragmatic book. Second, many patterns are obsolete with Java EE. That's why I wouldn't recommend it for a beginner. It's an interesting reading if you already have some solid background, if you can separate the good and the ugly yourself and want to learn more about the evolution of Java EE (understand, learn how things were complex in the past).
[3] Weaver J.L., Mukhar K., & Crume J.P. (February 2004). Beginning J2EE 1.4: From Novice to Professional. USA: Apress
I didn't read this one but, why the hell would you focus on the obsolete J2EE 1.4? Java EE 5 is out since may 2006, Java EE 6 has been released in december 2009. Just learn up-to-date stuff (i.e Java EE 6 or at least Java EE 5).
[4] Pandu D., Rahman R., & Lane D. (April 2007). EJB 3 in Action. Greenwich, CT: Manning Publications
Ahhh, finally a book not too dusty. Actually, I consider it as the EJB 3 bible. A must read if you are doing EJB 3 development (and if you master it, you should be able to grasp EJB 3.1 without troubles). But not strictly about Java EE (only the EJB part).
So, at the end, my recommended Java EE books for a beginner would be:
Yes, both of them, and in that order.
And for more specialized topics:
