Lots of good information expressed above. It's rare to see this topic discussed so well.
If I can summarize what I've gotten, with reference to the original question, what it boils down to is individual preference, among reputable ammunition manufacturers. What is the shooter comfortable with, in terms of holding a gun in his hand and getting the effects of the controlled explosion.
I spent a lot of time looking at the manufacturer's ballistics data for lots of different .38 and .357 cartridges, and came to the conclusion that it's a pretty wide and continuous selection of choices. You can go from mild to wild, and everything in between. There's some .38 special +P's that are more powerful, all things considered, than some .357 magnums. And, basically, all of them are deadly, when used properly. True, some are more deadly than others, but all of them will work.
My suggestion would be to get a box of each of several different cartridges of varying weight and from different manufacturers (and brands within manufacturers) and see what works for you, keeping in mind that what you use for target practice isn't necessarily what you'll use for daily carrying (although you should, of course, practice with that, too).
For example, if 158 grain .357's have a little too much kick in your 2" barrel J frame for total shooting comfort at the range, but are still within the scope of your ability to control the gun, you may still want to carry those rounds for defensive use, but practice with a 125 grain.
I, myself, have never heard the phrase, "full house" used in connection with cartridges; it sounds like marketing fluffery to me.