Hello Daniel,
It really depends on your location, so some info on your location would be helpful, but I currently live in the Sonoran Desert, so I do have a bit of advice. As for wildlife we have quail, dove,
rabbits (cottontail and jackrabbit), javelina, and
deer to name the major ones. When hunting for big game though it helps to have mountains in the area for glassing, otherwise it can be a big challenge out here. Also, most of the animals will go through the arroyos, so those are usually good areas to check for big game. Small game can be a little easier though because they only really come out at dusk and dawn and any groves, arroyos with a decent amount of trees, or some other cover attract them very well.
Also, as for animals go I currently raise
chickens and goats and have had success with coturnix quail. Those are mainly what everyone else keeps around here too, although a few people raise sheep, pigs, and ducks as well and they do just fine as long as the ducks have a constant supply of clean
water. Other animals to raise are guinea fowl,
cattle if you have the
land (longer horned cattle tolerate heat better), and turkeys (with just a bit more care) can all be raised just fine as long as they have sufficient food, water, and shade. Though, unless you have some real dense shade from a tree I wouldn't recommend to keep rabbits because they're a lot more sensitive to the heat than anything else I've raised, but they can survive with adequate shade and care. One thing to keep in mind is that varieties of poultry that are a bit smaller tend to generate less body heat and do better and for sheep the breeds that shed their wool in the summer do a lot better and they generally have less problems than sheep breeds that keep their wool coat year round. That's just about all I can think of right now, so I hope this helps and again it depends a lot on your location.