I think you should learn C first, because I learned C first. C gave me a good grasp of the syntax and gotchas with things like pointers, all of which flow into C++.
I think C++ makes it easy to wrap up all those gotchas (need an array that won't overflow when you use the [] operator and a dodgy index? Sure, make an array class that does bounds checking) but you need to know what they are and get bitten by them before you understand why things are done in certain ways.
When all is said and done, the way C++ is usually taught is "C++ is C with objects, here's the C stuff and here's how all this OO stuff works", so you're likely to learn basic C before any real C++ if you follow most texts anyway.
