Being in Texas you will be able to use a rifle. I picked up a used rem Model 7 in a .260 for my 6 and 10 year old boys to shoot. It fits the bigger boy great and the younger one can manage OK too. Both each took an 8pt. and a doe last fall.
This gun had some trigger work and porting done. The trigger work is great but the porting makes it REAL loud in a stand, protect those ears well.