Why not a .22 for plinking? You can't get much milder than that or much less expensive. If you reload, light target loads in .38 Special should also be good. .32-20 and .32 S&W Long will cost as much as .38 Special in factory loads and reloads will be only a little less expensive in handloads.
(.38 Short Colt would have no advantage in reloads, and factory ammo is almost unobtainable.)
Jim