This is a very common question, and there's two camps:

1. Learn C, then learn some C++. You won't appreciate Rust until you've felt the pain that it solves.

2. Learn Rust. Why bother going through all that trouble on your own when you can have the compiler help guide you.

and a third position:

3. Rust is still new enough that you'll find way more information with C, so you should just learn that even if Rust is better in a vacuum. Learning is easier with copious help and tutorials.

I personally fall in camp 2, and sometimes 3.