In my opinion, you should start with C++ as C++ has been said to be superset of C language and what you learn in C is fully available in C++.
One major thing backing my choice is that sometimes later you have to learn about the concept of Object oriented techniques, and this is where most of programmers find difficult to adjust, whose base being procedural languages like C, FORTRAN, or other. Even JAVA, C#, VB.NET all are based upon object oriented techniques from ground up. So if you have very sound knowledge of Object Oriented techniques, then you can learn any of these languages quickly.
One thing I want to share from my experience is that all the programming languages has almost same types of statements, but differ in syntax. Like there is "if..then...else" statement each in C,C++,JAVA,C#,VB,PHP,etc.
The major noticeable shift is in data types they support and other advanced features like support for pointers,operator overloading,etc.
One thing you should kept in your mind there is no shortcut to master any language, but if you master any one of these language (C++,JAVA,C#,or other Object Oriented Languages) then you can take on any new language easily as all have the major statement supported with few new advanced features.
I am giving the name of a book which would certainly help you as the most valuable reference book for C++ or JAVA -
1.C++ - The Complete Referecene (TMH)
2.JAVA 2 - The Complete Reference (TMH)
Hope this guide would help you to make your choice. 8)