If you want to seriously get into handgun hunting for deer or anything else, you may want to consider the T/C Contender or Encore. You can get an almost endless list of interchangable barrels from 17 mach 2 up to 45-70 and in lengths from 10" up to, i believe 15". The Encore chambers barrels in cartridges such as 308, 30-06 etc.
In my Contender I have barrels in 22 lr, 7-30 Waters, and 35 Rem. In a revolver or semi I wouldn't use anything less than 44 mag or possibly 41 mag. IMO I don't think the 357 has enough energy to humanly take a deer. I've heard of people taking deer with them but I wouldn't recommend it.
And you have to practice, practice, practice - and not just off a bench. Some type of shooting sticks or rest is a must for accurate shooting at anything outside of 50 yds.