Ruger BH in 44 mag should make a great choice handgun hunting for deer.
I started handgun hunting 50 years ago with a H&R Sportsman model 999 when I was gifted the H&R for X-mas 1974.
Since then I purchased a S&W 629-2 new 36 years ago for deer hunting, then about 7 years ago bought a S&W 460 with a 7.5" barrel from the Performance center.
44 Magnum is a awesome deer cartridge