I think if you are sharp and are having a good time with it, then C++ is an OK beginner language for you.
If you asked me the same question without having actually picked one to try yet, I'd suggest starting with Ada instead. It is just as powerful as C++, but far less cryptic.
Also its syntax was designed to be less error-prone, and it does far more compile-time and runtime checking, so you'll spend much less frustrating time debugging your programs. What really turns off a lot of a lot of would-be programmers is when they get nasty bugs they just can't find.
The main thing now that you are using C++ is that, once you get comfortable with it, you go out and try another language. Too many people get so used to one native lanugage that they can't see outside its borders. I can't count the number of people I've seen who hate all languages but their first, simply because they do things differently. But even if you were to stick with C++ as your main language for life, I guarantee you that learning Lisp will make you a better C++ programmer.