Re: OP. A lot depends on the range you anticipate for shots and the size of deer in your area. In my area a deer over 150 lbs. is a whopper. One of my church members shot a nice six point buck last week, he weighed about 128lbs. I shot a doe that was hardly over 100 lbs. Either one could have been handled with a .357 if the range had only been say 25-35 yds. However, the buck was shot right about 90 yds., the doe was shot at 128 yds., either shot would have been a tough job shooting off-hand under field condition.
I've used iron sighted revolvers for hunting small game, etc. for 30 years. Inside of 25 yds., a little 18-3 or a nice .38/.357 loaded with light mid-range wadcutters is just about pure poison. Most of the time I've always used a six inch 28-2. I've been using them off and on since 1980. They are wonderful. Load them with anything up to and including nuclear level loads... they just work. With 158 gr. JHP's loaded hot whatever you point it at will fall down. If it tries to get up, give it another round. That'll probably be enough. A 180 gr. cast lead bullet will give you tremendous penetration, useful if you need to take a raking shot. Take a look at Buffalo Bore ammunition as see if anything they offer is of interest. Their ammo is not for target shooting. But for hunting, it'll really do the job.
As far as revolvers, you cannot do any better for a hunting .357 Magnum than to find and buy a S&W 686. They are simply the top of the pile, the revolver that every other company wishes it made. The longer barrels will give you more velocity, always a nice thing when hunting. They are superlatively accurate. The later versions are factory drilled/tapped for scope mounting.
Just a thought... but for handgun hunting you might want to consider a Thompson Center single-shot handgun. They are available in a variety of calibers useful for hunting with barrel lengths that will work well. Mounting a scope on one of the TC pistols is no problem. The triggers are wonderfully crisp. Typically accuracy is outstanding. It's just a thought. The other day while hunting I looked at that doe after I shot her. The distance was about 128 yds., long for a iron sighted revolver. But, with a nice little scoped TC chambered in a appropriate caliber, I think that doe would have dropped just as dead as when she got hit with the 150 gr. .30-06 that I was shooting.