In a 357 - you can shoot 38 Colt Short, 38 Colt Long, 38 Special, 38 +P and 357.
In a revolver classified as being for 38 +P - you can shoot 38 Colt Short, 38 Colt Long, 38 Special and 38 +P
In a revolver classified for 38 Special - you can shoot 38 Colt Short, 38 Colt Long, 38 Special
Obviously, when shooting a "shorter cartridge" - such as a 38 Colt Short/Long or 38 Colt Special in a 357, you will have a slight "bullet jump" as the slug is not as close to the front of the the cylinder as the longer 357 cartridge is - it will will work just fine. I reload 38 Colt Shorts, Longs, Specials and shoot them in a 357 all the time. Just be aware that you can get carbon buildup in front of the cylinder throats which may make it somewhat difficult to chamber a 357 round in a cylinder if you've shot a bunch of shorter cartridges through it. Easily taken care of by cleaning your cylinder chambers well.
As far as "recoil" - normally the more "potent" the cartridge is, the more "recoil". i.e. you can expect more recoil out of a 38 + P or 357 than the standard 38 Special.
As far as "stopping power" - you'll get all sorts of opinions on that one. I normally carry a S & W Model 36 Snub loaded with 38 Specials. I have full confidence that for me, they are adequate. It was the standard cartridge for many, many years for Police agencies. I worked Ambulance as well as Rescue for a number of years and handled a number of "gunshot" calls - some fatal and some not. In my own personal experience, I saw wounds caused by a wide variety of calibers from .22, 9mm, 38/357 and .45 - as well as long guns. Believe me, they can ALL do a lot of damage and it's about "placement".
I used to have a Ruger LCR in 357 - I purchased the 357 so I would have the option of shooting 357s if I wanted to. I still found myself sticking to the 38 Spl. - but that again is a "personal" thing. The LCR is a good shooting snub - I just prefer a J frame Smith for my CCW.
Regardless of what ammo you decide to use (or your wife) - just remember - practice, practice and more practice on a regular basis. And practice with the loads you are going to carry. It's one thing to practice with something like a 38 Spl wadcutter at the range - but they are going to shoot a whole lot different if you are carrying 357 rounds for SD.
I reload, and I cast my own bullets. I like to load 38 Colt Shorts for plinking, fun range time. But, they shoot a whole lot different than my SD rounds that I usually have in my J frame. Just remember . . . while "power" is good as far as putting down an adversary, "shot placement" is more important. It does no good to carry with a potent 357 cartridge if you can't place your shots in critical mass and put the threat down if necessary to save you own life or that of others. Hopefully that situation will never occur.
The best thing you can do is to have your wife try the various cartridges in a LCR. If you have a range where you can rent one, have her fire a number of 28 Specials, 38 + Ps and 357s. That will be the telling point of what she should probably be carrying in it. She wants to carry what she can "manage" as far as recoil and being able to come back on target after firing. A lot of that will be based on her size and muscle strength.
I have a friend I shoot with when I'm in AZ during the winter. She is petite - maybe 5'4" and 115 lbs. - I'm just guessing. She has a hard time handling the recoil of my 38 revolvers - Smith M & P, Combat Masterpiece, Model 36, but she has a Sig P230 .380 ACP that fits her smaller hands well and she is "hell on wheels" when it comes to shooting it. I feel sorry for the bad guy if she is ever forced to use it and I've told her that many times. She got that way by "practice" and becoming very proficient with "shot placement".
Good luck to you and your wife - you'll get it figured out and I hope she enjoys her LCR if that's what she goes with. It is a nice SD wheelmen!