welcome tdstout. a 357 lever gun is great fun and I think you'll be happy with one even if you end up not hunting with them. true winchesters are very scarce and expensive. Practical contenders these days are marlin rossi and henry. (cinarron and some italian companies make guns tailored to cowboy action shooters, but for regular guys those are the big 3. well, really, big 2 and henry)
If it were 5 years ago, I'd say get a marlin 1894. But remington bought them a few years back and quality has gone downhill. all the way to the bottom of the hill and then into a pretty big hole. If you can find a used one they're terrific. Rossi is a fine gun. lighter and trimmer than the marlin, but does not scope as easily, and I just don't like the feel of the gun much. Maybe it was because I was raised on marlin. I don't know a lot about henry. they seem to have a decent reputation, but I'm out on the brass receiver.
all lever guns will benefit from an action job. It's not hard to take a gun from "meh" to "oooooh" with a little 600 grit sandpaper and judicious spring clipping.
accuracy is going to depend a lot on the ammo and the particular gun. with a scope off a rest with factory ammo I would expect any of them to print a 3"-4" group or better at yds. offhand, with irons, somewhat larger. (I see people on forums claiming 2" groups offhand with irons, but I'm more of a 12" group guy myself. maybe 20" if it's windy)
But as kewlz mentioned, use the search function, "which 357" has been discussed many times. And I'm sure you know, for a true hunting gun, a 30/30 is a much better deer caliber. On the used market you can dig up a marlin 336 for less than $300. Figure 400+ for a rossi and $550+ for a decent marlin.
