I started hunting weith a Contender back in the mid 80's with a 10" 44 Mag. It worked very well. I used 200 gr JHP bullets out of this barrel with good results and recoil wasn't too bad.
I sold that barrel and now own a 14" 44 Mag, a 10" 357 Max., and a 10" 300 Whisper. I've settled on the 357 Max as my #1 deer barrel. Good accuracy and more comfortable to shoot than the 44. The 300 Whisper is as light as I'd go for deer.
You must be a handloader to consider the 357 Max, in my opinion. If you planning to shoot factory loads go with the 44 Mag. Ammo is everywhere.