A lightweight revolver is a wonderful thing until you shoot it. It sounds like recoil isn't a big thing to you, but it may be to your wife. I know a couple of ladies who bought lightweight .38's. They shot them about 10 times, and put them away. Yes, they have guns, but they aren't any good with them because they won't shoot them... it hurts too much.
My wife has a S&W model 36 .38 spl with a 2" barrel. It's made of steel so it weighs more than those airweights. But with its Pachmeyer grips it isn't too bad to shoot. She is pretty good with it. And it's simple to operate.
Most women I know aren't that interested in shooting, so they don't do enough of it to really become competent with a semi automatic. Too many buttons, the slide is hard to operate, they can't stuff more than 4 or 5 rounds into the magazine because their fingers just aren't strong enough or tough enough, don't know where to start to clear a jam, etc. I don't know if your wife is like this, or not, but if she is, a .38 revolver is probably your best choice. I would then buy a good double action .22 revolver when you can afford it. With that she can learn to shoot safely, competently and accurately, without the cost or recoil of the .38.