Speaking for myself, irrespective of who wins I plan to buy .22 handgun for my daughters to shoot and 12 gauge for yours truly.
Get ur daughters a S&W M&P .22. It’s full size, fits the hand well and has all the features of a larger caliber handgun. I have one I use for training when I work with new shooters.
If you have never used a firearm I would suggest you go to an indoor gun range and rent different types of them, but above all find a good instructor first.
I grew up with firearms and had a cop-in-law that was an instructor for the department and was an expert marksman, by the time I was 16 I could shoot better than him but he was the one who taught me the basics, and we would go thru thousands of rounds of ammo as he lived in a rural area every week. Practice is everything.