Dr. Fresh, take a look at Corbon, Federal, Buffalo Bore, or Grizzly Cartridge. All of them offer hardcast loads that I'd say are appropriate for a woods gun. The heavier the better: 180 or 200 grain is good. The theory is that heavy ammo with lots of momentum can break bone & penetrate deep, which is important in a defensive scenario where you can't choose your shot on an animal.
If I was hunting as opposed to carrying a handgun for animal defense, I'd prefer copper hollowpoints since these do a better job on the vitals. I like 100% copper bullets for this since they won't leave any lead in the meat. The only copper ammo I know about is put out by Federal and Corbon.
For small game (grouse, squirrels) I've found that .38+p is plenty adequate.
Take this with a grain of salt, but here are the loads I'd prefer in .357: Federal's 140 gr Barnes Expander ammo for game hunting, Buffalo Bore's 180 gr LFN-GC HC ammo for animal protection. One practice I like is to load the first few chambers with defensive loads, and the rest with hunting loads.