I know what you're saying; I was looking for something very similar not too long ago to shoot a lot and save money. Tried some .22 rifle and .22 conversion kits.
In my honest opinion, .22 training rifles are overrated. Too much is changed to be an effective supplement; your muscle memory will adjust to the lighter recoil, quieter crack, shorter bolt travel, etc. For training purposes you're far better off just doing dry fire drills in your living room. It's free, totally safe, and when done correctly will dramatically improve your shooting ability.
If you're really set on a range toy to shoot cheap and for your grandkids to shoot with you, then I'd say go for it. If price is an issue, you could also just get the .22 coversion kit and mags to swap out in your existing rifle. I think they usually run around $100.