I came into programming the old fashioned way. I started with Basic then moved to C and then C++. I personally would not recommend you learn C++ until you first learn the C way of doing things.
I would disagree with that. C++ has a particular way of doing things and it's best that if you are going to learn C++, then you learn idiomatic C++. Learn the C way of doing things, when you decide to learn C. For emphasis, C != C++. Not even in a "C is a subset of C++" sort of way.