RE: 410 question...
If she intends to go hunting deer don't get the 410, it is very limited. Probably pistol and bowhunting ranges which is about 30 or 40 yards. And to be honest a pistol or bow would work better at those ranges. A .357 handgun has better ballistics and bullets than a standard 410 slug. Probably more accurate as well.
Many want to get 410's for beginner shooters because of the low recoil, but to be honest they are more of an advanced shooter type gun. They have limited payload and range due to the small shells and usually a tighter choke.
A much better shotgun would be a 20 ga. Even better yet if she wants to hunt deer get the H&R ultra in 20 ga. If you order it you can get it with a bird shot barrel as well so it is more versatile.
Another option would be a mossberg bantam pump in 20 ga, better yet a combo model with a cantilever rifled barrel.
If you just want to go in the back yard and shoot things a 410 is fun and low on recoil. However the shells are pretty expensive for what it is. If you want her to hunt step up to a 20 ga with a modified choke or better yet screw in chokes. You will be happier in the long run.
Or for target type stuff you could get her a ruger 10/22. They are fun to trick out and play with. Another option would be a 17 HMR or HM2. A bit more expensive to shoot, but they shoot flatter and are usually more accurate. I love my Savage 17 HMR and it only cost $200 before the scope.
If money is no object get a 20 ga auto like an 1100 or 11-87. My girlfiend is not very big and she shoots trap with a rented 20 ga 1100 youth model. She also has a single shot 20 ga remington SPR 100. Recoil is not that bad with low velocity target loads, even in a light gun. And 20 ga shells are much cheaper than 410 and 28 ga shells. Plus you can get them anywhere with a wide variety to choose from. I own a winchester 9410 (410 lever action) and getting shells for this gun kills me. Very little selection and the prices are a joke compared to 20 and 12 ga shells.
I will say it again, for deer I would go with a mininum of 20 ga, and that is with modern sabot ammo out of a rifled barrel. Or you could get her an inline muzzle loader and you could tailer a load for her.
Or if she likes pistols a decent .357 revolver would work well on deer out to about 40 yards or so. And she could shoot the .38's out of it for practice.
Sorry for rambling.
Paul