Basically if you want OpenGL in Java, then writing your own bindings from scratch would be ludicrous. LWJGL/JOGL does it very well, and both have been maturing over many years.
Regarding higher level libraries, like LibGDX, Slick2D, jME, etc. that depends on your game's needs, your goals, etc.
Here's how I view things:
LibGDX - for 2D/3D games on desktop/android/WebGL
jME/Ardor3D - for 3D games on desktop; more mature than LibGDX with 3D capabilities (i.e. model loading, terrain, etc)
Slick2D - for small 2D games and fast prototyping; especially nice for beginners coming from a Java2D backgroundTextureLoader
- if you want to just use OpenGL but don't want to write your own decoders for audio/image, you can use these utilities
Slick-Util - like above, contains audio/image decoders, as well as other utilities (Color, font rendering).
LWJGL/JOGL - this would be as "library-less" as you get with OpenGL. It will be a lot lower-level concepts, but great if you want to learn OpenGL from the ground up or if you want maximum flexibility/efficiency for your game engine.
I'd suggest starting with a simple 2D game, using LibGDX or Slick2D.