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I agree,Ruger 10/22 is my fav hands down,accurate,reliable and infinite upgrades and parts available.

But on the 410 I will break with the crowd and say its a good gun.Its perfect for training and small people,you can step up later to 12 gauge if you decide you like shotties.

You dont mention defense but 410 has a lot of fans for that too,its smaller everything makes it suitable to all size of users I hear too,yet remains a formidable weapon,never say never,bad things happen..... (Dont own one,know Fans of gun who do)

I think your choices are perfect for beginners.For training children,again PERFECT choices in my not so knowledgeable opinion.

Other thing is join a rifle range and you will find all kind of experts who will HAPPILY school you,and at least here our range rats LOVE women shooters,they will have you shooting their guns (Boy is that fun!),which means you will get to see every possible gun and what fits YOU to a tee,range membership is a very good thing.

Mrs now knows what she would like going forward,especially true with handguns as they have to fit right,etc,as you know.

But do consider legislation and stay up to date,if you see a certain gun or something may be banned your way you might not want to own that weapon and then face hurdles to ownership.