An additional idea for your consideration: I own a fair number of Smith (L and N Frame) and Ruger (GP100 and SP101) revolvers, primarily .357 magnums. I believe the .357 magnum alternative is adequate for deer (as others have correctly stated, accuracy is THE KEY).
However, I recently bought a Smith 610. This N Frame is simply terrific: very accurate, great quality, fit and finish, superb reliability and durability, AND IT FIRES BOTH 10MM AND .40 S&W ROUNDS (just like .357s fire both .357 magnum and .38 special loads). I would respectfully suggest a five-inch 610 would be ideal for deer, with essentially as much muzzle velocity/energy as a .357 magnum, a heavier and larger diameter round, and a flatter profile for longer distances. In addition, this would provide your arsenal with another “twofer”, with .40 S&W ammunition for target and plinking work abundant and inexpensive.