jad0110
Keep in mind that in many states (not all), .357 Magnum is the minimum caliber for hunting said game.
Don't get me wrong, I think 9mm makes a great plinking and SD round (with proper ammo selection). I don't own a 9 currently, but would like to pick up a Hi Power or CZ-75 one day in that caliber. But you'll also probably have a hard time finding 180 grain hard cast semi wadcutters in that caliber. In other words, the .357s has a much wider envelope of performance potential with power levels and bullet selection.
To meet the OPs criteria, IMHO, the a 4" medium frame .357 would be the best fit. .38 for moderately priced plinking, can reliably fire shot shells for pest control, big and stable enough for hunting and small enough for concealed carry.