I bought "Developing Games in Java" by David Brackeen, as well. It seemed like the friendliest looking java games book in the store. Now that I've looked around a bit, I've learned that his methods are most likely outdated. The book still holds promise, mind you. It's definately a good book for teaching the basics of game design. Just be aware that:
I skimmed the book and looked round his site a few times. My impression was that he's no expert on this stuff, and probably I'd have advised him not to write a book just yet - to wait a few years till he had become more knowledgeable about this field. I wouldn't recommend it to anyone I was teaching simply because of the number of bad habits it seems to encourage (like multithreading a game, etc). There didn't seem to be anything in there that was original enough to significantly distinguish the book above all the others out there, and all the university courses that you can access free on the web.
...just first impressions. YMMV.
As to what binding to use, the war continues. I think Java3D is pretty much out, but there might be some support there still. I tried JOGL, but couldn't really get a handle on it. Since then, I've started playing with LWJGL, and found it to be quite excellent.
This is a major topic
(I like the choice of words - "the war
I have similar feelings about the API's but for very different reasons. Again, this is just opinion, but I'll add it here because I want to make one point in particular: Java3D is not *yet* a good idea (Sun recently resurrected it, but let's give them another 6-12 months before making a judgement on whether they've made something useful for games dev; they've emphasized that's not their aim).
BUT Xith3D, the same API but a different implementation (because no-one had Sun's source code for Java3D) is going strong. It is also a bit easier to use than J3D and a bit faster IME (there are good reasons for this, and it's nothing to do with bad coding by Sun).
I too would recommend LWJGL because, compared to JOGL, it's effectively about 2 years more mature. When you look at the kinds of bugs, and the kinds of missing features, and the amount of thought that's gone into the design, it's going to take about that long (IMHO) for JOGL to reach the same level of quality as LWJGL.
I say this as a person who *always* prefers official or Sun-sponsored techs, and so I tried with JOGL for some time. Really, I tried. But it just kept smacking me in the teeth for my efforts. LWJGL certainly has it's own bad habits and is far from perfect, but my experience so far has been that it's considerably nicer to you than JOGL. Then again, I haven't tried JOGL in the last 6 months, and a lot could have changed in that time.