I second the suggestion for you to find a range that will rent revolvers...in 4", 6" and 8 3/8" in .357 mag and .44 mag ...so you can judge for yourself how you can handle the recoil, and whether you like them or not. ( or a buddy that has some of the above).
To me .357 mag is ok on deer / maybe black bear...but its getting marginal ...but a .44 mag is a lot tougher to shoot accurately, especially with a follow up shot.
Lots of SA/DA guns out there ...from Ruger, S&W etc.../ or you can look at some Single Action models....like the Ruger, Colt, Freedom Arms...and especially in Freedom Arms, I see quite a few used ones, with scopes mounted, that would make a good hunting platform ( in .357 mag, .44mag, .454 Casull, .475 Linbaugh, etc...) ....kind of depends on your budget.
But even if I intended to hunt with a handgun / I'd probably carry a rifle as well ....maybe a lever action in .357 mag or .44 mag ...like the Henry, Marlin, etc...quite a few of them out there...and its fun to have a handgun and a rifle chambered in the same caliber..( I think at least).
I have a lot of revolvers in .357 mag and .44 mag ...and with some arthritis, etc...I like shooting the .357 mag a lot more than the .44 mag...