Were I to attempt to take a whitetail w/ a .357 revolver, my choice would be a 158 JHP. My concern would be that the lighter JHP's would not offer sufficient penetration if a shoulder bone were struck or the angle was not ideal and one ended up with a raking shot. Some of the lighter JHP are intended to limit penetration....and that is not a concern on big game bullet. The 180 class slugs do not seem as common in the places I frequent, and I'm not sure they are necessary on 150 lb deer, but they would work too.
You will have to shoot well and pick your shots to match your ability range wise. If you cannot hit a 9" pie plate near every time at a given range, you have reached your limit.
Lots of folks have pulled this off, unfortunately, not me.