I learned to clean coon by pulling and scraping as much fat off the meat as you can. Then I roast it, just like a beef or pork roast, with all the same additions--taters, bell peppers, onions, carrots, etc-- but do it all on a rack so the grease can run off. I've served it to people who thought it was turkey or pork. Got some coon quarters in the freezer now; maybe I'll thaw one up and cook it for church dinner this Sunday....
Beaver, when I can get one, the same thing--just roast it like a, well, roast. Have served that to people who thought it was good beef.
Only tried groundhog once--not many around here--and it was a really sweet meat. Wish there were more to be had.
Squirrel and rabbit isn't 'exotic' here, it's just regular people food. My step-daddy wouldn't eat them, because he had to live on it during the Depression, and (according to him) only 'poor people' ate that stuff. Guess it traumatized him to be considered poor back then.
Possum I've thought about trying, but every time I seriously consider it, I remember the time I found an old cow carcass out in the timber. Took a stand about 50 yards off, hoping to get a shot at a coyote or some crows when they came to scavenge. After a while, noticed some movement under the hide on the belly. Thought it was expanding gasses, and was all set to watch it pop; but instead, a possum chewed its way through the hide and came squeezing out the hole. Kinda messed up any idea of trying to eat road rat. Acebow