TheCheezWhizard:
My entire extended family is from Louisiana, and my uncles love to hunt, so I've been around game meat since I was a child. Venison, rabbit, and squirrel were the most common, all of which are delicious. I moved to Pennsylvania in 2010 and never really got into hunting myself, so most of the meat I eat nowadays comes from either the grocery store or the Internet, but I still eat a lot of venison and rabbit because they're relatively easy to find commercially. Squirrel on the other hand is impossible to find; I've been searching for years to no avail. I miss it so much haha.
Anyway, I'd highly recommend those as a place to start. Alligator and turtle are fantastic as well, though I'm not sure if they meet the technical definition of "game."
La. native here and come from a hunting/fishing family, so I can relate to all of it :-)
Deer roasts slow-smothered in a cast iron pot (much like you’d do a beef roast) are the best. If done right, you’d never know it was wild game.
I’ve had fried alligator tail before. Has a texture much like chicken (the old saying is true, ha) but is best wrapped tightly and refrigerated a while.