CDC is good; FBI UCR is good.
But you're stepping into a world of arguments with the questions you want to address.
John Lott has the research on CCW/crime "More Guns, Less Crime", two editions. Gary Kleck has the Defensive Gun Use (DGU) - Point Blank: Guns and Violence in America. Both have other popular works available.
Now, it happens I don't find the arguments against these publications persuasive, but you would do yourself a favor by doing some Googling around to see the criticisms, and understand them, and be prepared to respond. A number of the critics are not, strictly speaking, anti-gun, but have methodology and internal consistency questions worthy of consideration.