What would be a good standard load, not +P for plinking and self defense?
Jacketed or cast?
3" J frame.
For one load for both uses, I would suggest a 148 grain Double Ended Coated Lead Wadcutter under 3.3 grains of Titegroup. This load in my M-36 J frame 2" barrel gets me 754 FPS and 187 Ft. Lbs. energy. Recoil is mild. With your 3" barrel you will get a little more velocity. For self defense, you really may want to up that a little unless over penetration is a concern. Several companies manufacture these bullets, such as Missouri Bullet Company. ACME may also have them, not sure. I know that Bayou does not.
I know you are asking for one bullet/load for both uses, but for defensive purposes, not +P, I would use a 130 grain HST jacketed hollow point wadcutter under 3.6 grains Titegroup. The hollow point cavity is huge. Midway currently has them as blems. I don't know of any other source. They are made by or for Federal for their HST ammo. In my 2" barrel, I get 803 FPS and 186 Ft. Lbs. energy. However, that bad boy usually expands to about .65 - .70 caliber and with 10 - 12 inch penetration, also with mild recoil. They are quite accurate out to 7 yards. That is as far as I have tried them, however I have heard that they are reasonably accurate out to 50 feet. This limitation is due to the huge hollow point cavity. That is what I now carry in my snubbies.