I've heard more than a few people mention the value of using rat traps to trap animals during a survival situation. Dave Canterbury from Dual Survival swears by them. They are small, lightweight, and very easy to set. They should be good enough to catch rats, mice, chipmunks, squirrels, birds, and similar sized animals. They are cheap now and will be super valuable after the SHTF, which makes them great barter items as well. Buy dozens of these and set them up everywhere. Also, set up dozens of snare wires and dozens of cage traps. See what works best for your game and your location. Practice now and be good at it after the SHTF. Remember to drill a hole in a corner of the trap and stake it to the ground so your meat doesn't hobble away.
...or you could always spend 1hour setting up a figure 4 dead fall :-/