First, each state is different, so you will have to look into your state's laws regarding what game is available for hunting.
Two critters that are easy to hunt in the summer are cottontails and jackrabbits. These can be procured using a bow and arrow, heavy-duty slingshot, or .22 rifle. With any of these weapons, obtain proper instruction in safety and become proficient at marksmanship. I hunt only to feed myself or my family and have little regard for sport or trophy hunting. Cottontails provide a more tender meat and are best made into a stew. A single jackrabbit can provide a lot of meat for a survivor, but it is a tough meat. When we have it at home, I find it best prepared by
In other desert regions, there are pronghorn antelope, mule deer, and bighorn sheep, but small game is a good place to start for the beginning hunter and much easier to obtain once the fundamental skills are learned.