A gas semi auto will be the softest shooting. Hard to beat a Remington 1100 LT 20. In your price range used in very good shape, not too heavy, and soft on the shoulder. If you need a shorter length of pull, they have youth stocks available too. No way an inertia gun will shoot as soft. There are some lighter 20s, but they don't have that steel action sleeve that really soaks up recoil.
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