First of all, I presume that you wish to shoot .357 ammo instead of .38 special, and that this is why you want a larger, heavier revolver than the airweight J frame in a pocket.
A revolver that I have come to like in this role is the S&W model 66 snubby, a stainless K frame gun with a 2.5 inch barrel, 6 round cylinder and weighing about 32 ounces empty. I carry it in an OWB belt holster because IWB carry for such a short barrel gun doesn't really buy you much concealment, and I find it uncomfortable. The model 66 is out of production, but lots of used ones are on the market for about $400.
I use Remington 125 grain .357 magnum Golden Sabers in the gun, which give muzzle velocity of 1220 fps in a 4 inch barrel and probably 1100 fps in my snubby barrel. The trigger on this gun is excellent in either DA or SA, and it handles recoil very well because of its weight.
With a little practice you can point shoot the gun without using the sights and easily hit center mass on a profile target within 10 feet, which is probably the main self defense usage of a gun like this anyway. But for longer shots the light SA trigger and adjustable S&W revolver sights allow excellent accuracy.