I would go for .38 wadcutters for your intended purpose. Should be superbly accurate in your 3" barrel, easily controlled for fast repeat shots, deadly on rabbits, quail, and squirrels, and an adequate manstopper. The biggest advantage is the mild recoil, enabling frequent practice and training sessions to gain proficiency. Low ammo cost is another plus, encourages target shooting practice.
The snubby guns tend to have widely changing points of impact with load changes, so using the same load is important to gain shooting confidence and proficiency.