OpenGL is pretty advanced, so it may not be the best place for a newbie to start.
Swing/Java2D is good for learning GUIs and the basics of a graphics API (images, shapes, paths, etc).
Other than that, it is not very good as a game library. For a complex game, you end up needing a lot of boilerplate, such as game loops, graphics context and buffer strategy setup, input handling setup, texture atlas tools, tiled map loading, etc. You will end up struggling with huge differences in performance across systems, and generally very poor performance compared to what you might expect from an application in 2012. You will also need to struggle with JavaSound which is pretty awful.
So I’d suggest learning the basics with Java2D – develop some simple tic-tac-toe games, make various software tools so you can understand GUIs and programming concepts, etc. Once you’re ready, you can move onto game development with a library like LibGDX.