I also suggest that you take a look at slick2d. The thing is that slick2d is a library built on top of lwjgl, which basically is (or part of it is) a wrapper for open gl in java. You can start by using only the command set from slick, but when you dive a bit into the open gl materia, you can start using opengl together with slick.
First of all, don't start a big project but get comfortable with the topic. Start creating prototypes for displaying images, rotating them, handle user input etc. When you have grasped the basics start with a simple game. Try to implement a small game you know. Could be minesweeper, breakout, snake or whatever, but first of all you shouldn't start a too big project, as it ends up often in a mess (I started with slick2d about a year ago. When I look at the code I wrote then a shudder runs down my back XD). Try to complete the game and polish it (include main menu, highscores, maybe saving depending on the game, sound fx and music)..
When you completed that game start with something new, this time a bit bigger, and try to improve your skillset...
Another great tip: Hang around in forums and look for useful information... I tend to go to here and http://www.java-gaming.org and look for interesting topics, even if they aren't directly related to my current problems, I often find very useful pieces of code or explanations, which I store in a seperate folder in my bookmarks. Every now and then I go through that list and see if I can use something of it.