Pick what you like, and make sure to finish stuff (that's a bigger challenge then learning a language's syntax)

I disagree. It must be a framework that makes games. It doesn't have to be C++. In fact, it shouldn't be C++. And you should just go for desktop games for now.

Go for mobile platforms, iOS and Android, they are the big thing at the moment. Be under no illusions however, game programming is complicated. Why not use an engine like you described. Many languages can be used, C, C++, JS, HAXE, JAVA.... It's not so much about the language rather the underlying graphics libraries that can support the language.

I think your first priority should be to make a game from start to finish.

To make your problem as easy as possible, start with tools and languages you are most familiar with, so you can concentrate on the game itself, rather than fighting your tools and programming language.