Free: Contests & Raffles.
Ruger American Compact rimfire. Mine will put 10 shots in a one inch group at fifty yards with the ammo it likes. Simple little 4 power Leupold scope is money.
Agree with scotsman on Winchester 69a. My first rifle and the peep sight is great to build confidence. Light enough for youngsters to hold steady and magazine fed is easier than a tube fed for kids.
Find a classic Winchester model 69a. My dad gave me one when I was 10 years old and I still have it now. My kids and grandkids learned how to shoot with it and it’ll still shoot 1” groups at 50 yards. The original 4x Weaver scope still works fine. Granddaughter got her first chicken-stealing coyote with it too.