Didn't realize how harsh that sounded, excuse me for that.
But anyways, for that game type. From what I've seen in google, it's like a flying sim or something? So I'd either suggest jMonkeyEngine or LWJGL, depending on the amount of work you want to do. You can get the different information about those two from the different threads here.
No worries. By match 3 I mean the ones where you move some object into a pattern of three to make the block disappear. There is a boatload of them on Facebook. I guess Bewjeweled is the first one. The latest giant is Candy Crush. There are all sorts with candy, fruit, you name it.
I'll look into LWJGL. I would try something more abstracted, but I like to stay low level, at least until I understand what's going on, and I see myself writing lots of boilerplate code nor falling in to the NIH syndrome.
I have seen the many libraries available. Like Java EE, there is a big stack with lots of possibilities. Some lend to 3D, some 2D to 3D, some 2D, and so on.