I've hunted from east coast white tail to Arizona Mule Deer and Texas hogs with handguns and while I'd even risk cover shots at Mule Deer here in Arizona with a .357 I'd rather something more for hogs.
If I exclude SA revolvers and semi-autos - which I always exclude from MY notion of hunting - I'm left with generally .44 & .41.
I started with .41 so it holds a special place for me and I am very confident in its abilities within the parameters I choose to apply for handgun hunting. So, I'd not turn my nose up at it in your search.
However, reality says to start and most likely end with a .44 in DA that will be scopeable should you eventually choose to go that way too. Personally, I don't like them on a hunting handgun but I do get others liking them.
Now, I know there are fellas out there happily hunting with semis, single actions, smaller calibers and the like. It's just not my bag, Baby!
Nope, a stainless, DA and of either Wesson flavor; Dan or Smith, seems like the ticket for me. Load it down to Special and below or up to full-house magnum.
My current favorite is a 629-5, 6 inch. Of course, I'd turf it to the safe in a NY-minute for a Dan Wesson.
Now too, "Why DA only, Todd?" Because, in general and especially when there's blood on the ground.... the whole food chain can and often does, dramatically shift. I don't want to be thumbing no SAs when I'm on the menu.
Todd.