LWJGL and JOGL are the very lowest level graphics libraries you could choose, and there's a fairly steep learning curve (though, fortunately, plenty of examples and documentation). Both are just wrappers around OpenGL. LWJGL provides a more complete solution for games in one package and can be entirely independent of AWT on Windows.
MonkeyEngine is for 3D stuff and has its pros and cons - just spent 6 weeks watching it in use from the sidelines. It has some curious and irritating design flaws but it works. It's essentially based on LWJGL and abstracts away most of the fiddly stuff for you letting you get on with writing a game.
Java3D is a bit behind the curve these days. Take a look at Xith3D which has a very similar API.
There are a couple of other 3D scenegraphs out there as well - Ardour (sp?) and Aviatrix spring to mind.