I can't quite bring myself to use a .357 on deer. I know a lot of folks use it successfully - but I wonder how many failures don't get talked about. I just really like the extra bit of insurance that a .44/.45/.50 provides.
Having said that, if I ever decide to do it, I'd consider one of two strategies. The first would be a JHP driven as fast as I could manage, with the knowledge that if I wait for the perfect broadside heart/lung shot I should have a good result - and that if I get impatient and don't wait for that shot, I might have a real damn mess on my hands. The other strategy would be a big solid, like a 180 WFN GC, and a shot where I can break bones. The latter is my usual M.O., though with bigger bullets. I consider it the most reliable - and least spectacular - shot available to the revolver man.
As far as hardness: if the bullet fits the gun, it doesn't really matter. If it doesn't fit the gun, it doesn't really matter either. In the former case, just about everything will work, and in the latter case, nothing really will. Likewise, hardness isn't going to make a difference in terminal performance either, as long as an extraordinarily hard bullet doesn't shatter. I personally would stick with my usual 1-16 tin-lead, and utterly ignore the "hard cast" nonsense from the bullet advertisers.