Recoil is a significant consideration for a person who is getting started with shooting. I've seen huge men who have developed a significant flinch from shooting even moderate recoil weapons such as a .45 ACP. When you give a gun to someone who is new to shooting and small framed, starting them with a powerful firearm is best case scenario going to result in them developing an instinctive flinch, and often results in the person deciding shooting isn't for them and either never practicing with their defensive gun or ditching the sport all together.
People who claim that anything smaller than a 9mm Luger is ineffectual against a human in a self-defense circumstance are suffering from a condition known as "ittybittywilly disease", and it is a common affliction among ignorant old men who've spent a little too much time inhaling lead fumes while casting their own wadcutters. These are the same men who think you need a 416 Rigby to take out a white tail at 50 yards and buy a v-10 with a 2 foot lift for their bi-weekly drive to the tavern to spend their social security checks. There is no need to bust out a cleaver when a paring knife is well suited to the job, and you don't need a magnum to take out a human sized attacker.
There is no such thing as a "girl gun", and many intelligent men and women who are capable of reading actual ballistic information find a carry gun chambered in .22 WMR, .380, or .32 to be more than adequate.
If you are comfortable with the recoil and the size of the gun itself, sure, get a .40, a .357 Sig, or a revolver in .38 or .357 Mag. They are fun, but you don’t need something like that to get the job done. Don't worry too much about "knock down" or "stopping power", those are relative terms with little real world relevance. If you shoot someone, whether with a Barrett, a Derringer, or a slingshot, chances are they're going to stop. And contrary to what the movies tell you, even if you shoot them with a .460 they aren't going to be knocked down so much as fall down because they no longer own an abdomen.
.22LR is not only adequate, it is actually an extremely effective defense round. The unique ballistics of the standard velocity rounds allow the bullet to penetrate the target, however they don't have enough power to go all the way through. The bullet tends to bounce around the body or skull of the animal hit with it, thoroughly scrambling the guts to a mushy pulp. There are many who don't believe it because they don't want to, but there are endless reliable sources such as autopsy techs/ coroners who confirm the unique terminal ballistics of .22 rimfire rounds inside a human body.
.380 is a good lower recoil round and there are a ton of great carry gun options in that cartridge right now such as the Ruger LCP, the Sig P238, or the Walther P380. To make one of these even more comfortable, you can get options like aftermarket Pachmayr grips and low recoil ammunition such as Hornady Critical Defense. I'd stay away from rounds such as the .25 or .32 because they are borderline obsolete and difficult to find ammo for, though they do also have manageable recoil.
If you are particularly recoil sensitive, consider a .22LR. Revolvers such as the Ruger LCR are a fantastic choice, however people who are particularly sensitive to recoil often also have less hand and wrist strength, so the trigger pull on a gun like that may be arduous and not practical. I'd recommend holding and reading up on guns like the SR22, the Walther P22, and the Browning 1911-22 which are all small, reliable (make sure you get the right ammo!), and shoot the comfortable and deadly .22LR round.
As an aside to something I saw earlier in the thread, “kick” is a common and perfectly acceptable colloquialism for recoil. Don’t let people talk down to you because you are new to shooting. There are a million and one things to learn and you deserve to be commended for joining the community of responsible shooters who want to be able to take care of themselves. We all learned from the bottom up, and not everyone was born into a situation where you learn it gradually as you grow up. It is a lot to take in and most shooters love the chance to help people who want to learn more about shooting and firearms.
The most important thing for you to know when buying your first concealed carry gun is that you are comfortable and confident with it, you will be deadly with it. If you are afraid of your own gun, it is next to useless and could be more of a liability than a tool. Have fun and good luck to you!