The best place to start reading Captain Marvel is at the beginning of Carol Danver's 2012 series. That series, the first under writer Kelly Sue DeConnick, completely redefined Carol Danvers and Captain Marvel. Books 1 & 2 especially are some of my favorite issues of all time, both inspiring and beautiful. They also serve as a great lead-in to Kamala Khan, Ms. Marvel.
US Air Force Major Carol Danvers was in a very 1960s-comics accident which fused her genes with those of the alien Kree superhero Captain Marvel (real name Mar-Vell). She gained super-human powers and became a hero under the name Ms. Marvel. Long after the death of Mar-Vell, at the start of her 2012 series, Carol took up Mar-Vell's mantle and became Captain Marvel herself.
Captain Marvel (2012) and further, in chronological order: