Does the range offer rentals? If so, get a .22, because I assure you, if you start her with a .40 S & W, she'll never want to shoot again. And I'd agree, a revolver would be easier for her to deal with.
My dear wife had never shot until age 70, she had been around guns, her late husband was a shooter. He passed away many years ago, and I was out of shooting for quite a while after we got married (well, if a "while" is 20 years). I got started shooting again, she got worried about crime in our area, and she decided to learn shooting. Her first firearm to shoot was a .38 Special revolver, an old Ruger Service Six. She's had both shoulders operated on, and has limited hand strength to operate a semi-auto. She did fine with a .38 without any kind of complaint about recoil. Your mileage may vary.
Just start your sister on a firearm you don't think will turn her off because of recoil, and stand back and watch. If she feels she's overcoming her fears of firearms, and is actually enjoying shooting, expect to have a partner for a good long time at the range.
Consider getting her an hour or two of instructor time, I have every confidence you know what you're doing, but a patient instructor who is not related to her may give her more confidence than learning from you. I got a couple of hours of instructor time for my wife, and I'm sure she learned more from him than I could convey to her, and she didn't learn mistakes I'm sure I am capable of doing from time to time.
Just a thought.