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I think there should be a lingua franca. It should be something clear and simple. It does not have to be BASIC. It shouldn't be BASIC. It should be something that has a hope of being relevant in 10 years. It need not be relevant in 20.
I'm not sure what that language should be, but I rather like Python.
But Python needs a module to handle very simple graphics like you had on the Apple ][.
As for some of the other things you want, you should look into Open Source. One of the biggest advantages of Open Source is that all the code that makes things work is right there. You can tweak it and see what happens to the program. This is one of the reasons the one-laptop-per-child project uses it.
I cut my teeth on BASIC, it's true. But that's just because it's what was there. Even as a child I vastly preferred assembly, Pascal, C and Action! to BASIC. None of those used line numbers. Assembly was much closer to the heart of the machine.
I don't think VB with it's fancy 'enterprisey' programming environment that insulates you from what's actually happening is any good. I don't think C++ with its awesome complexity is any good. I would go for a 'scripting' language. Sure, you can type in a few lines and have the earth move. But you can also type in the little simple programs from a textbook and have them do something on the screen right in front of you.