If so, what ammunition or bullet type/weight would you prefer?
Yes, I consider the .357 out of a 4" barreled revolver to be "sufficient" within a reasonable range. The range will be limited by your ability, under field conditions and positions, to put every shot into a 6-8" target (the heart/lung area)...every time. Personally I would not shoot past 50 yards as a maximum with a 4" .357 revolver regardless of whether I could hit the heart/lung area.
Depending on the size of deer in your local I would use the 125 gr Win or Fed HPs if the deer are 125 lbs or smaller on the hoof. If larger then I'd look at the Speer 158 gr Gold dot load. If handloding I use the 125 gr XTP HP and load it over Blue Dot to a genuine 1400+ fps. That load works for me on deer up through 150 or so lbs. On larger deer I would again look at the Speer 158 Gold Dot bullet loaded to 1200+ fps. However, if your revolver is a medium frame then you might want to stick with the 125 XTPs at 1400 fps. A soft cast HP'd GC'd 150 -160 gr bullet at 1300 fps will also do nicely. Do not expect the deer to drop at the shot. Continue to shoot additional shots as long as they are presented.
Practice shooting, a lot, from field positions (sitting, kneeling, standing with and without support to know your own abilities to put every bullet in the heart/lung area) and also practice with an adjustable bipod (shooting sticks - I prefer Primos Trigger Sticks) if you "still hunt". Then when you think you are good enough to hunt with the revolver go practice some more before you go hunting.
Larry Gibson