Ahhh! First off, the good thing about comics, especially Marvel, is that you can almost start anywhere and the book will fill you in on what’s been happening in the character’s life in the first page or even within the story itself, so there’s really no right or wrong place to start.
Secondly, okay, so, I’m not a Carol expert or anything because I’ve only recently started adoring her myself, but I’ve been reading the current Captain Marvel run by Kelly Sue DeConnick and it’s pretty great (as in “yes, read it”). There are some tie-ins to the storylines within it, in Avengers Assemble (also written by DeConnick) - issues #16-18. More coherently, here’s a little reading order for the volume so far:
Captain Marvel #1-#12
Avengers Assemble #16
Captain Marvel #13
Avengers Assemble #17
Captain Marvel #14
Avengers Assemble #18 (though this also ties in with the current event Infinity, it tells you the outcome of something that happened to Carol, so I’m including it here)
So yeah! Honestly, that’s where I would start, but if you’re interested in other comics she’s appeared in, here’s a huge reading order: http://marveloki.tumblr.com/post/34031345504/ms-marvel-reading-order
I hope this helps some!