38-40 +P+
The 38-40 fires a 40gr bullet out of a case holding 39gr of water. Thats a slight bit more capacity than 44 mag, but it is neutered by a 12k psi limit. 44 mag runs up to 3 times that pressure. So then enters the 357/44 Bain and Davis. A 44 mag case necked down to 357, which propels a 160gr bullet at 2000 fps out of a 10" contender. That would be a heck of a round for hunting, if i didnt have a rifle and was stuck with just one pistol. But thats not a part of the criteria...
In all reality, 44 special works well for me. I carry a 5 shot 3" revolver in 44 spl every day. It can be downloaded for smaller vermin and can certainly take a deer at the right distances.
38 spl would be second, followed by 10mm