Greg-
I am a writer and know the issues involved in getting guns right. It will add a lot to your story acceptance to get details correct. I have stopped reading books when it became apparent that the author didn't know what he was talking about.
I think your logical choice is a Colt or S&W snub .38. If it had a light alloy frame (lighter to carry) it would be a Colt Cobra. The steel frame Detective Special is the same gun, except for the material in the frame. Heavier, but more durable, if shot much, and recoils less.
My first choice would be a S&W Chief's Special with round butt and in steel frame. I don't think a girl would want a Centennial; they're ugly and the hammer can't be cocked for a more precise shot with less disturbance to the aim. That would be especially important if she was just learning to shoot, although the average gun carrier then probably didn't practice much unless she was serious about the matter. The average girl might fire one box of ammo and not shoot much thereafter. She might not shoot it at all unless a man took her out to shoot.
I'll answer your skeet gun question now. Either Remington M-870 or a Winchester M-12, either in skeet grade with better grade wood, a ventilated rib on the barrel and a recoil pad. Such a gun would also be effective for hunting to about 25-30 yards. Farther out, you'd want a tighter choke.
Don't give her a Browning automatic: they weren't regularly imported here prior to 1954. Colts discontinued at the end of WW II would still be available, some previously unsold. The choice would be between the .25 auto and the .32 or .380, both in the same basic model. Only caliber differed. How big is her purse? The .25 is less effective, but fits almost all purses, save the really tiny ones.
Look up these guns and see pictures. Try to handle them. Something will tell you which she had, if you know your character. You also need to know the person who gave her the gun. He may have chosen what he'd use, or given her a .32, thinking that was all that a girl could handle. That was very common thinking among men then, even on police forces.
A lot of the advice that you'll get here will be be less than optimum. I once asked about guns that members would have chosen had they been on the Challenger expedition depicted as being in 1919 on a syndicated TV show, "The Lost World." About 70 % of the guns chosen were unlikely, some not even being made then. I wrote fan fiction, and included some guns not seen on the show, in the hands of characters whom I created for particular stories. I thought that someone might hit on one that I'd missed that would fit a particular character. I needn't have bothered. I also enjoyed speculating on what I'd have chosen, had I been on the expedition. It's fun arming characters, but you do have to know guns well and know your characters. And their times...
Keep in mind that a gun found in a burned car might have been damaged by the heat and be unsafe to use, except as evidence.
Good luck with your book. I have one about half completed. I wish the rest of the story was as easy to write as the gun data.
T-Star
P.S. I'll share a humorous gun-author story. In, "Savages", Shirley Conran armed characters with Smith & Wesson "Chick's Specials."
I assume that she either misheard what an advisor told her, or that her consultant was having fun with her. But a knowledgeable reader could tell what she meant and the book is otherwise excellent. I highly recommend it to those who can find a copy, maybe at the library or used book store. It is an exceptional story of survival near Papua-New Guinea after a terrorist attack. Conran got most of her data from British military survival experts.
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