You can find .270 ammo anywhere that sells ammo in Alabama. Don' t overlook .22 and 12 guage (seriously). 30-30 and 30-06 are also very popular. I know more people who keep over 100 rounds of 7.62 x 39 than .223
I think you kind of hit the nail on the head, whatever they sell at Walmart would be the best bet. 30-06, 270, 308, 30-30, 9mm, .45, 44 magnum, 12 guage, .22 aren' t likely to sell out, but it never hurts to keep a couple of boxes on hand.
Another route to go is buy a cheap rifle that shoots cheap surplus ammo and buy the ammo in bulk. You can get ammo for cheap mosin nagant or mauser 98 rifles for a few hundred rounds for under $50. I have a couple hundred rounds of 8x57 ball ammo for if I ever needed my kraut rifle, though realistically, I' m probably a thousand times more likely to burn through it shooting milk jugs or clay pigeons than ever use it in a social breakdown crisis.