I have killed deer with an M-1 Garand, M-1A, FN-FAL, SKS and an AK.
Just pick a soft or hollow point (I like the Remington Fusion SP) in ~150 gr.
A state can have varied terrain so it is hard to tell just what you'll be into, but for a brush gun the SOCOM and 3X would be dyn-o-mite!!
WARNING- Most states have a magazine capacity limit and I'll bet Alabama does. You will need to find a mag that is legal to hunt with, or you can make a 20 round legal by taking it apart and putting a wood block under the follower that would make it conform which is what I did for the FN-FAL. But be prepared for a game warden to check you out if he sees you.