Im against hunting, so i wiont and im not able to help you with that. but first, buy a simple training bow. even one of these cheap gift shop ones, just to know the basic aiming and feeling. I got two brazilian bow as a kid, so i could handle more complicated bows later, as they helped me with the stability and the aiming, and the action of reloading and shooting itself. Start with these. thene go to more complicated ones.
Some sort of compound bow for hunting would be good. But specifics are going to depend on what you plan on hunting. I'd assume you'd be hunting either turkey or deer, so you'll want something that has a good pull weight and can propel the correct type of arrow at a speed that can kill.
But just go to a sporting goods store and ask the people working there. if theres a Bass Pro Shop near you, you should definately make the drive out there. Besides the employees being very helpful, it's a cool place to walk around for a few hours. its a camping/hunting/back packing/canoe/kayak/outdoor paradise.
I live in the northwestern area of arizona, on I-40, south of the grand canyon and on the western edge of the part of Route 66 that has Radiator Springs on it (peach springs in real life). (if you can't understand my directions, I live in Kingman)
I am not sure what wildlife is around here, but the Hualapai mountains probably have game, although I am not sure if their is an extra cost to hunt there.