Go for it. You have my full support and encouragement. Pick up a copy of The C Programming Language, 2nd ed. , by Kernighan and Ritchie, affectionately known as K&R2; and add
to your .bashrc to get the most out of it. Feel free to ask questions if you run into trouble.
alias cc='gcc -W -Wall -ansi -pedantic'
It is true that C++ has lost a good bit of its popularity to Java, but both are still pretty widely used and therefore useful to know. I won't venture any advice on that because I know very little C++.