Java EE 6 is really amazing. The only problem is that it's about 2 weeks old, and there is only 1 container currently offering it's features -- Glassfish.
I have nothing against Glassfish, I use it all over the place, several production instances, I love the product and the project.
That said, the details of JEE 6 do not translate back to JEE 5. Some do, many do, but the Web Profile, Servlet 3.0, the new Bean types, JPA 2, etc. Those aren't there.
So, by learning JEE 6 first, you're simply constraining yourself to a single container. More are coming, but they're not here yet.
Tomcat, JBoss, OpenEJB, Glassfish, Jetty, Resin, Geronimo, etc. all work well with the JEE 5 spec (at least those parts of the spec that they support, Tomcat doesn't have EJB for example).
I can't think of anything in JEE 5 that wasn't carried forward to JEE 6. JEE 6 made some very old aspects optional, and those you simply wouldn't learn today anyway. JEE 6 made some JEE 5 stuff even easier (packaging notably, EJB Lite for example).
Learn JEE 5 now so that you can actually apply what you learn in a variety of environments, rather that learning JEE 6 now and discovering you may not be able to use much of what you learn.
No single book will teach you what you need to know. Servlets, for example, are a nice foundation, but for anything larger than a couple of pages or endpoint, you will want to use one of the many 3rd party frameworks, or JSF, and no book covers the core and then a framework on top of that.
The JEE 5 tutorial is good at getting the foundations down, my major complaint is that they don't show you the source code. Rather they expect you to just download and run it. It's not discussed in the tutorial. I've found the Head First books to be pretty good.
For web programming, raw Servlets are important enough just to understand the request/response cycle but you don't need a deep understanding to make a leap to a 3rd party framework.
I'm a big fan of Stripes for an Action framework (vs a component framework), and the single Stripes book available is excellent (making choosing that an easy choice).
I can't suggest a Component framework book, and I actually would not recommend one right off. The component frameworks truly bury the HTTP core request/response structures. They bury them for a reason, and they gain value BY burying them, but I believe to be effective you need to have a solid understanding of these concepts early on. That's why I don't suggest learning a Component framework first.
The JAX-RS REST framework, included in JEE 6, but readily installable in JEE 5 or any servlet container, is excellent. Arguably it is what Servlet 3.0 should have been. But I don't know any books for that.