First.......K frame.....
The model 15 is fine. The model 10 is the standard K frame with fixed sights, but if you want the adjustable sights (I would)the model 15 would be the way to go. I had a model 10 but traded it for an L frame 686. For fun shooting I would try to get one with a barrel a little longer than the snub, unless you plan to carry it. I love K frames, but I wouldn't want to conceal carry one.
The mod 36 needs practice and discipline to shoot well beyond a few yards. It's a close in defense gun. Great gun though, I have one and wouldn't trade it.
The K frames are easy to handle and shoot, even for people not used to handling guns. The .38 special round is a pretty ideal as ammo runs from light target to Plus P whammer blammers. So choice of ammo is very important depending on what you want to do.
If you are just planning on shooting for fun, the K frame would be ideal for anyone, wife included.
IF you decide you want an L frame mod 586/686 make sure to get a barrel, no longer than 4-5". My 686 is just a tad nose heavy with a 6" barrel, though it holds and shoots great. My wife LIKES big revolvers because they soak up some of the recoil. If you shoot .38s or light .357s in the L frame they are pretty easy to handle.
IF you are familiar with shooting and use ammo that can be handled by the person carrying it, a J frame is pretty ideal for SD.
There are light alloy J frames, but they will kick a lot more. My wife got one she can't really shoot without very light ammo. With heavy loads it smacks my hand pretty good. My son fired one shot out of it and the first thing he said was, "There ain't no way Mom's going to be able to shoot this gun!"
For an ideal light carry gun that is easy to shoot, the M&P Shield semi auto 9mm is as good as it gets. It's double action only. The trigger on the Shield is close to a single action, which makes them easy to shoot. There are other guns in that same category that work about as well depending on what features you want. If I can say ANYTHING negative about the Shield, the body is very slim, which is good for carry, but feels just a little harder on the hand. However, I find the Shield to be a VERY comfortable gun to shoot. It's plenty light and can hold 8-9 rounds depending on the magazine used. I like the 9 round because it gives more for your little finger to hold onto.