In my opinion, if you have an idea for a game in your head it doesn't matter what you write it with (at first), C/C++, Java, pen & paper... Pick the language you're more comfortable with, prototype and test your game idea, once you have a rough sketch and know what you need to do, throw the prototype out, design the gameplay & architecture and then start coding the actual thing. Don't optimize until after you've got most or all of the functionality working (in general, there's always minor bugs to hunt) and you actually see where the bottlenecks are.
I've seen it happen over and over again, game programmers are among the worst premature optimizers ever, trying to squeeze out a few cycles from something trivial, while missing the biggest bottlenecks and then optimize some more (in the wrong place). I've also found myself guilty of this many times. I'd say don't pick C++ (or Java for that matter) because of the speed, you can get very good performance out from both, if done "right". If need be, you can always switch to another language, if the language itself is really the bottleneck or really preventing you from doing something. Java isn't automatically slow and C++ isn't automatically fast, you can go (very) wrong with both. I used to root for C and C++ in everything, but after having worked with Java for quite a while, I really don't miss all the hassle that much.
There are lots of (already optimized and fairly easy to use) game engines available for both languages, so there's no need to roll your own... unless you really want to. In my experience, most hobbyist "game programmers" tend to be more interested in the technical side of things than in the actual game (myself included) ;) Once all the technical hurdles are done and you get that nice model/bunch of sprites/particle effects running with some shader-effects, the enthusiasm seems to fade away... But don't let me discourage you, game programming is very fun, even if you never actually finish anything (I wouldn't call any of my own projects finished).
I haven't coded any games for a while, but for C++ 2D SDL is a good candidate, other option could be SFML, or if you want a lower level touch with OpenGL, you could try going with GLFW + SOIL + some audio library. For full-blown 3D, I'd say try either OGRE or Irrlicht + Irrklang (there are probably loads of others too).
In Java, there's at least Slick2D, Golden T Game Engine and for lower level access, LWJGL (although I think you can access LWJGL via Slick2D also). For 3D, someone recommended jMonkeyEngine to me, but I've never tried it.