Depends on where you want to put the balance between ease of use and low-level.
LWJGL is low level, and with the exception of a few helper functions, is just a wrapper for OpenGL/AL/CL.
Jogamp is similar to LWJGL.
LibGDX is a library built on top of LWJGL or Jogamp, depending which backend you want.
Skills learnt from LWJGL can be easily transfered into other C-family languages with OpenGL bindings. Jogamp should be the same, but I don't have any experience with it.
LibGDX is a Java-specific library. However, it's main benefit is the ability to export to Android and HTML5.
Would you recommend LWJGL? Is it common, mainstream, reliable and generally good?