Having one drop in it's tracks is very rare, unless you can pull off a head or spine shot. The trick is to take your time and make a good lethal shot, then wait QUIETLY for +/- 30min. before making any racket that might spook the deer. Usually the deer/hog will wander off a little ways and lay down and die - - easy to track and find. But if spooked they can easily manage to run a long way through thick cover you can barely make it through.
In rifles I'd choose the .308 over the 7.62x39. The .308 shoots flatter, has more power, and will take just about any game in the U.S. While the 7.62x39 is a great brush round the .308 is "more lethal" at +/-50 yards and allows you to reach out to 200 yards if needed, it is much more versitile than a 7.62x39.
Your .357 should work fine in close. Just my oppinon, but I prefer a cast core or jacketed soft point (JSP) bullet over any kind of hollow point for hunting. Winchester makes a couple:
and Federal has a 180 cast core that should preform very well.