It really depends on what you want. JME is a 3D engine thy will take a lot of the low level work off your hands and provide you with a nice interface to interface with the code, so use it if you don't like to code absolutely everything. However, its not really a 2D engine.
LibGDX is a great high level library, I personally love using it. It allows you to utilize OpenGL without having to write all the low level rendering code, so use it if you want to program most of your game, but are ok with not delving into the "hardcore" low level graphics. Its also mainly 2D!
LWJGL just "ports" OpenGL over so you can use it in Java since OpenGL was written with C languages in mind. If you use LWJGL, prepare to have to google a ton and work on the low level code for a while before you can start thinking about actually setting a game up. I've done it before, its actually fun to learn all about OpenGL and shaders, but I don't like having to rewrite my render engine because my new game has different requirements than my old engine.
There's also Slick2D, but its not as... (Trying not to stay a flame war) good or used much anymore. LibGDX is almost its successor, in a way. Slick2D is pretty easy to use, but I dont know if its ok for me to recommend it!
Good luck on whatever you pick!
I think i will go with libgdx, but should i use OpenGL with it? i didnt quite understand. Is there any other libriaries that i should use with libgdx?