.36 cal flintlock.
Mostly you will be eating squirrels, raccoons, rabbit and birds. The big game will last only a few weeks.
If tshf and there are still millions left alive, the woods will quickly be hunted out. Hopefully you can take enough meat to survive until the planting season. Also, you will to turn it all to jerky so it does not spoil, since I assume there will be no refrigeration.