Using what I have

I think the 357 with a decent 180 gr bullet should be a fine on whitetail. Shot placement is critical so you would have to limit your range to your level of accuracy. For me that amounts to 50 yards with a 357.  The biggest thing you can do to help yourself is practice so you can hit your intended target.
If you are looking to hunt larger game then I would want something that starts with a 4.

As with anything used for handgun hunting it depends on distance, bullet placement and bullet performance. The .357 is good with any lead bullet from 158 grain on up to about 180 or so. Velocity is important but not as much as placement in the vital killing zone. I think Skeeter wrote about some good shots with his .357 on those southwestern deer, but he did say he didn't generally recommend it except for experienced shooters. I guess that means practice till you are confident you can do it. Good luck, Chris

Does bullet weight make a huge difference in POI in a .357?  If I'm going to practice a lot I'll need to reload.  If heavier bullets will work better on game I figure I should buy big bullets.  Will hunting loads be hard on the gun if used for extensive practice?

Bullet weight does change POI a bit but you probably will want to shoot mostly lighter weights and loads a lot to get the practice in then switch to some of your hunting loads to dial in POI for hunting. The main thing is hitting your target. It's not necessary to pound you or the gun for practice. Chris 

The 357 has a long history as an effective and accurate game getter. It all began with Col. Wesson and the registered magnum. He successfully hunted all kinds of game with the then current factory load of a 158 lead semi-wadcutter. The 357 is deadly, and has been so since it arrived in 1935.
Today we have a number of very, very good bullets to choose from in the first magnum-and this just increases its effectiveness-IF USED WISELY. Always look to premium bullets designed for your intended game. Avoid el cheapo bulk bullets. Hornady, Barnes, Swift, and others make great hunting bullets. They are not budget items, but they will do what you need them to do.

The 357 does not have the ability to deliver the same shock as larger caliber cartridges, but it does not suffer from the same level of recoil, either. Recoil sensitivity is one of the biggest obstacles to correct shot placement. While the 357 is a major caliber, it will not wreck your elbows and wrists, and this allows longer practice sessions with hunting loads, which is what you need if you are going to develop a load that will work for you.
As always, stick to basics. Evaluate honestly what works, and not just what you want to work. Do not cut corners, develop proper marksmanship, and the 357 will work just fine.

I started out with a .357 the first year my State allowed hunting with a handgun. what Mak said was spot on and mirrors my experience. nothing more to add.

Checked out the Alliant website yesterday.  They have a new magnum pistol powder, MP300.  They have a load for a 170 gr jacketed bullet rated at about 1600 fps.  Anybody try this powder?

AZ:
The heavier the bullet the higher the POI. Here is a better explanation than I can make with thanks to Iowegan at RugerForum.Net:
 
"Well guys, here's what really happens. When the
powder burns enough to generate the pressure needed to move the bullet, the
weight of the bullet and the velocity of the bullet create momentum, which is an
"action of motion". According the Newton's third law of motion: "For every
action there is an equal and opposite reaction", the opposite reaction will be
"recoil". So ... recoil starts as soon as the bullet starts moving and
because the bullet accelerates as it moves down the bore, recoil will increase
significantly until the the moment when it exits the muzzle. After the
bullet exits the bore, another force is at work called "jet blast" where the
pressure inside the bore vents and continues to push the muzzle in the direction
of movement (up). Because the bullet has already exited the muzzle, it will not
be affected by jet blast but the muzzle will rise even more.

Recoil
always pushes the gun in the opposite direction of bullet movement at the same
momentum rate as the bullet exiting the muzzle. As an example, a 44 Mag 7 1/2"
Ruger Super Blackhawk revolver weighs 3 lbs. A 240 gr bullet exits the muzzle at
a velocity of 1350 fps. Momentum is computed by weight (in lbs) times velocity
in fps so in this case 240/7000 times 1350=46.3 lb-f/s. The momentum of the gun
is identical so you can compute recoil by dividing 46.3 by 3 lb (weight of the
gun) = 15.4 lb-f/s.

In order for recoil to be "straight back", the gun
would have to be designed as a straight object. Rifles are not quite a straight
objects due to "stock drop" but are pretty close so most of the recoil is
straight back with just a little muzzle rise. Any handgun will be a "L" shaped
lever where the fulcrum point (pivot point) will be centered at about the same
place as the hammer's pivot pin. The length of the gun from the pivot pin
forward to the muzzle forms one leg of the "L" and the the length from the pivot
pin to the bottom of the grip forms the other leg of the "L". These two legs
have a leverage ratio. If the grip leg was exactly the same length as the barrel
leg, the ratio would be 1:1 so each inch of rearward movement would raise the
muzzle by the same amount as the the bottom of the grip. Assuming the same grip
length, short barreled handguns have more muzzle rise than long barreled
handguns due to this "L" shaped lever ratio.

Average velocity in the bore
will influence muzzle rise. The longer the bullet spends in the bore, the more
time the muzzle will have to rise. The bullet starts out a 0 fps and ends up at
muzzle velocity. Using the above example for a 44 Mag 240 gr bullet @ 1350 fps,
0+1350=1350 so the average velocity will be 1350/2=675 fps. The barrel is 7.5"
long (.625 feet). Divide length by velocity (.625/675) and you will find the
bullet spends .00093 seconds in the bore. You can calculate other barrel lengths
or velocities and see the difference in time. When ammo is loaded with heavy
bullets versus lighter bullets to max velocities, the powder charge for heavier
bullets must be reduced or chamber pressure will exceed limits. With the added
weight of the bullet and less powder, heavy bullets will have a lower muzzle
velocity and will spend more time in the bore, which in turn means the muzzle
will rise more.

So in total, you have several things that affect muzzle
rise before the bullet exits: length of barrel versus length of grip, bullet
velocity, bullet weight, weight of the gun, not to mention the person shooting
the gun. The good news is ... you don't have to be a math major to figure out
muzzle rise .... all you need is a laser boresighter. With your gun sighted in
with your desired ammo at the desired distance, just aim at the target like you
normally would with the iron sights. The laser dot will show up several inches
lower than your point of aim. Measure the distance between the laser dot and POI
and that will indicate how much the muzzle must rise is needed to compensate for
the sights. This is very easy to do with a scoped handgun. If you change to a
heavier bullet and sight the gun in at the same distance, there will be a
notable increase in the distance between the laser dot and the POI, which proves
the theories above.

You can do a similar test with just a yardstick ...
it just won't be as refined. Place the edge of a straight yardstick with the
back end of the yardstick on your rear sight and have the yardstick rest on your
front sight. Stand back a few feet and you will see the angle of the barrel is
well below the angle of the sights. The factory sets the sight angle to
compensate for muzzle rise with a standard factory load. This is called "sight
registration" where POA=POI, even though the two angles are obviously
different.

Edited to add:

In conclusion, if you compute momentum,
which is velocity x bullet weight in pounds (grains divided by 7000), the load
with the highest momentum will always print higher on the target at 25 yards or
closer. At further distances, bullet drop starts to affect trajectory so a load
that prints higher at 25 yards may print lower at 50 yards. It is not unusual to
see a lighter bullet at a much higher velocity (more momentum) print higher than
a slower heavier bullet but with normal factory ammo, heavier bullets usually
print higher. "