I have 2 smokers and continue to learn with each time i get one out. The green egg i have was a present my wife got me after i had a lot of frustration keeping the temps up and constant with a Bradley biscuit smoker. I now pretty much only use the egg and I feel like i am doing what i wanted all along at this point. there are some awesome forums on just this subject and full of information.
Game meat:
I have done Nilgai, white tail, ferrel pig, duck, turkey and it works great on everything. I use a robust flavor chip on venison and everyone likes it. It is good with simple rubs. To keep it moist as much as possible, i always brine everthing, religously. It is a huge difference.
Best thing i ever got to enhance my fun with smoking was buying a duo grill/meat wireless themometer (mine is geen egg brand but does not matter who makes it). I can watch the meat temps and know that the smoker temp is without constantly checking the meat and do so from in the house if i have a long smoking time. I highly recommend getting one since it will improve your success.....wild meats do well under cooked vs. over cooked so if in doubt, pull it off the heat and call it a day...
have fun. My smokers have added to my overall outdoor experience..