RE: .22 or .177 pellet gun
i'd consider this in your desicion. the equation for KE is =MV^2
Mass is give a "1" value, but the velocity is squared. small increase in speed will help the power aspect more than a medium increase in weight. Remember in football how the little guys always seemed to give hits that equalled the 230lbs middle backer?
personally id go with .177 because in the end where talking about rabbits! not deer or even coyotes. I bet many a small lad has "konked" a rabbit with nothing more than a slingshot and lots of luck.