A few comments:
First, thanks to those who mentioned me.
Second, this may or may not matter to the original poster (teal) but quite a few of the writers mentioned so far were NOT gun writers. Instead they were hunting writers.
Those are not mutually exclusive occupations, but a gun AND hunting writer is still a gun writer. A hunting writer may mention guns in passing, but is generally not as technically oriented as somebody more interested in hunting guns.
A few years ago I wrote an article on books essential to understanding the history of hunting rifles--then expanded it a little in a chapter for GUN GACK II. This isn't necessarily a list of the most entertaining hunting-gun books, since some are pretty technical, and for more immediately practical than historical books I would certainly include a couple already mentioned, Bob Hagel's GAME LOADS AND PRACTICAL BALLISTICS FOR THE AMERICAN HUNTER and Finn Aagaard's HUNTING RIFLES AND CARTRIDGES. (My originally new copies of both eventually started falling apart. I replaced Hagel's with a new reprint, but Finn's book is held together with at least two kinds of tape.)
Here's a list of the historical works, listed in the alphabetical order of the author's last name:
Craig Boddington: SAFARI RIFLES IIGen. Julian S. Hatcher: HATCHER'S NOTEBOOK
Elmer Keith: RIFLES FOR LARGE GAME
Larry Koller: SHOTS AT WHITETAILS
Bryan Litz: APPLIED BALLISTICS FOR LONG-RANGE SHOOTING
Charles Landis: HUNTING WITH THE TWENTY-TWO
Jack O'Connor: THE HUNTING RIFLE
Stuart Otteson: THE BOLT ACTION, A DESIGN ANALYSIS
Philip Sharpe: THE RIFLE IN AMERICA
John Taylor: AFRICAN RIFLES AND CARTRIDGES
Harold Vaughan: RIFLE ACCURACY FACTS
Townsend Whelen: THE HUNTING RIFLE
The Litz book is included not to encourage long-range hunting, but it because it corrects many ballistic myths believed by many if not most hunters.
For wingshooting I would pick Bob Brister's SHOTGUNNING: THE ART AND SCIENCE. For handguns, a combination of Keith and Skelton.
There would be a different list for HUNTING books.
