I think you should define what kind of programmer you want to be. Web? System? Algorithm?
You already know programming a little, so you should decide easily if you want to do web apps, a new document format or some audio codecs.
I would suggest you start with python a very strong language with a very simple syntax (extremely close to pseudo-code). It also has a lot of modules covering a lot of fields. So you can easily find your way. Don't worry, it won't be a lot of new things. What you already know in Java and C++ will help you a lot.
Start by working on some easy problems first. I find
Project Euler will give you problems with incremental levels of difficulty. Or you can work on a simple thing like a chat program, or a calculator. You can build on top of that.
A good way to start could also be at looking at our
Programming Exercises. They would give you cool problems :)