I started shooting a .22 handgun at a very early age of 10, I hunted squirrels and rabbits, it was not tell I turned 21 that I considered getting into big bore handgun hunting. My first choice was a Ruger Blackhawk in 357 Mag. I practiced with 38 specials for a long time, and then moved up to the 357 Mag. It was not such a big increase, and the recoil was very manageable.
I went handgun hunting that year and killed my first spike buck with a handgun 28 years ago. I hunted one more year with my 357 Mag and was again successful. I then got the urge for a larger handgun and moved up to a 41 Magnum Ruger Blackhawk. Once again the step up was not a real big step, and I had great success using the 41 Mag and it was not long before I wanted to move up in bore size, and the 44 Mag is where I was for quit some time. Still in the Blackhawk, I did not see a need to change guns, as the Ruger's were working fine.
Eventually the 44 Mag became boring to me, so the 454 Casull was my next caliber of choice in a Super Redhawk, then from there I went wild.. 45 Colt, 480 Ruger, 500 Mag, 460 Mag, 510 GNR, 475 Linebaugh, 410 GNR.
I have always had a love for single action revolvers, I do however own quit a few double action revolvers, but I would say 75% of my handgun hunting is with a single action revolver.
The thing about handgun hunting people have to understand, you have to put a lot of time in at the range, and practice at the range you intend to take your furthest shot. You have to become very proficient at that range. Also know the limitation and effective range of each cartridge you choose, and aim for the heart lung area, and use a good bullet construction.
Personally I don't use hollow point bullets for hunting. I use hard cast bullets for all my handgun hunting needs. When I first started out with my 357 Mag, I used jacketed soft point bullets, and they work good. But not all the time would I get a good pass through, which is what I always wanted. So when I switched to hard cast bullets, I was hooked on all my game being shot with hard cast bullets. Also reloading your own bullets let you dial in your gun to shoot it's best in my opinion.