what is the sport running these days? i paid $679 for mine, and i haven't regretted it one bit.
the AR, like the 10/22 is certainly a gun that grow with you....you can change it up over and over.
i'd throw the mini 14 in the mix for the same price range as the sport. the mini is a great gun that could be another option. i like my mini 14 even more than my AR (preference).
imo, you have the family well protected with the shotgun for the imediate future....in the long run, i think you would be happier with the AR or with mini 14.