I've used my three Contender frames for over 27 years hunting big game in Alaska and Texas, along wtih more IHMSA silhouette matches than I care to count. For me it is the ultimate SS hunting handgun, and I've tried my XP-100, Encore, etc. The advantage is the smaller size and lighter weight...it is simply easier to carry when hunting. The others are certainly excellent handguns, just not my cup of tea - varming hiunting is something different.
I use a scope exclusively when hunting, and my favorite is a 4X. This works surprisingly well close up and out to 200+ yards as long as the hunter is familiar with it. I don't use my 2X scopes anymore as I feel handicapped; the closest deer I've taken was under 10 yards away so it is possible to shoot well at close range with a 4X....
IMO only amateurs shoot a scoped T/C with one hand; the pistol is just too heavy in hunting trim and no one can shoot it as well with one hand. I always place the second hand under the barrel, gripping the forend. This is simply more accurate, and there is no problem hitting yourself in the face with this technique; even JD Jones uses it when firing his HandCannons. Grip the forend firmly and it helps keep the rise in recoil down and absorbs a lot of recoil.
Barrels are easy to change and if you have the tools handy it takes less than two minutes. Chamberings suitable for deer include the 7-30 Waters, .30-30, .357 Maximium, .35 Remington, .41 and .44 Magnum and the .45-70 in factory barrels. Custom tubes allow almost anything practical. My favorite is the .300 Savage, firing a 150 BTip at ca. 2400 fps. Recoil is not bad, accuracy is unbelieveble, and it kills well from 10 yards to over 200 yards. I've used many chamberings, and the .35 Remington and .45LC are the others I use most. Still, at one time I held the world handgun record Sitka Blacktail, taken with a .25 Bullberry; very little recoil and extreme accuracy. Any reasonable cartridge will do. Range is limited by the shooter, almost never by the cartridge.