Picking out a gun for someone else is a lot like trying to buy them a pair of shoes when you don't even know what size they wear.
Here are some considerations:
1. How big is your daughter physically? My wife is 5' 100lbs with small hands even for a person of her size. She carries in a Beltster belt with built in holster Her CCWs are a S&W 3" alloy J frame with the old style pencil barrel in 38 Special and a Walter PP in 32ACP. We also tried a Kel Tec for her but she didn't warm up to it. My former wife who was only a bit bigger used a S&W 681 as a CCW but her fingers were as long as mine. Admittedly wife number 1 carried in her purse as there wasn't a gun belt made that fit into her idea of fashion. Obviously a big difference for not a lot of size difference between these two ladies.
2. How is she going to carry or is she going to actually carry at all? If she is actually going to carry on body weight is more of a factor. If she is going to bury the gun in her purse, weight isn't nearly as big of an issue. This also goes to size as well.
3. How is her grip strength? Can she comfortably rack the slide on an autoloader?
4. How often is she going to shoot? If she gets into shooting, an autoloader may make sense. If she is only going to shoot when you drag her to the range, you want a revolver with its less complicated loading, unloading, making safe and firing procedures. Be honest in your appraisal of what is going to happen, not what you want to have happen.
If you have to have a general recommendation, go with a steel frame revolver. I like Bodyguards. That gives her the option of being able to thumb back the hammer both for an easier shot and a deterrent. The sound of a hammer cocking won't do as much as a sound of a shotgun being racked but it is unbelievably loud when a revolver is pointed in your direction. Another option is a M60. I have a 3" chambered in .357 with adjustable sights that I have carried quite a bit. While this is the S&W forum, I also like Ruger SP101s. The steel frame guns weigh more but recoil is less. 38+P in an alloy J frame aren't comfortable to shoot even for someone who shoots a lot as a general rule. While I realize you can practice with target wadcutters and keep recoil down, sooner or later she has to shoot some real deal ammo to know what she has in her hand and where it hits. If your daughter is not terribly petite (I'm not being rude but there is a heck of a difference in a lady who is 5' 100 lbs and one that is 5'8" and 125lbs, both of which are slender) you might want to look at a K frame S&W. I really like 3" barrel M65s. I don't particularly care for the 2.5" barrel M66 because the ejector rod won't give you a full stroke on a .357 round to absolutely clear the empties. That is a personal quirk of mine and a lot of S&W fans will probably howl at me. If your daughter is really interested in becoming a dedicated shooter, then in addition to the above, you can look at autoloaders.
S&W 3913s are good pistols, they are big enough to use, small and thin enough to carry. I'd avoid Glocks. Even the M19 is pretty much a full size gun which is harder for a small framed person to conceal. My wife can't make one work because of small hands even though she can run her Walter PP well. They are also fairly thick due to being double stack guns which makes them harder for a lady to conceal on her person. Keep in mind, you and I'll buy our pants a size or so larger to carry an auto IWB. We won't care if the seat is a little baggier than we need but I bet you never asked anyone if a particular pair of pants made your butt look big?
Finally regarding choices, I would avoid micro guns. Yep a derringer or a 5 shot mini revolver in .22 LR beats the heck out of no gun but they are hard to hit with past contact range.
I'd gather up some options from shooting buddies to let her shoot and see what she likes to shoot as opposed to what she likes to look at in the store or get her to a range with rental guns. If she has never shot before, get her out with a .22 and some range time before you even start the process.
Hope the analysis helps. Think about who and what your daughter is rather than thinking what is cool to you. That's hard to do sometimes. I have seen a lot of guys at gun counters trying to push what they want on the lady in their life not realizing what they were doing and not realizing that they weren't doing her any favors to buy her a gun that she couldn't make work because it was too big, recoiled too much etc.
Jim Keene
PS You're doing a good thing helping make sure your daughter has a higher level of security.