I teach a lot of kids, AKA young people to shoot and have found that my SW 10 shot revolver works like a charm.
A SW 686 I think it is
Simple, easy to use and can't get away from them as fast as the autos when they are first learning.
Once they run a few hundred thru the revolver, then on to the old Ruger Mk1 Bull and then onto something in .38 and finally up to whatever they can handle based on age and ability.
And it gives me an excuse to shoot .22 all I want!
without comments like, shooting that mouse gun again!
Ruger and or SW are fine choices and can be had in your price range.