If you are considering only loaded ammo, I have shot a few boxes of Hornady 44 Special 180 grain JHP/XTP's and found them pleasant to shoot and accurate. This load has a muzzle velocity of 1000 fps and the XTP has a good reputation as an accurate hunting bullet.
Ideally, you should be hunting out of a tree stand, where distances are short, and approach your shot selection like a bowhunter would.