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You at UAB? It is a boring ass school and city but there's good people here and there. Anyway, Birmingham is kinda far from most of the real wild spots but there's some great places within 2 hours or so. My personal favorite is the Sipsey Wilderness section of Bankhead National Forest. Good backpacking trails, beautiful waterfalls (pic related is a shitty phone shot of Feather Hawk off the 202 trail), some cool old graveyards. Talledega NF is cool too but in my experience a little more crowded, its proximity to the interstate and Cheaha State Park attracts more of a weekender crowd while Sipsey is more serious outdoorsy sorts. Talledega does have the Pinhoti though if you're into thru-hiking. Alabama also has a state public lands trust called Forever Wild which seems to mostly be geared towards hunting land but has some cool tracts which allow camping, Walls of Jericho in Scottsboro is my favorite but a very tough hike.
If you're going to learn to hunt, start with hogs. They're a horrible invasive species here and provided you have a hunting license you can hunt them in the daytime with any weapon any time of year on most public lands. A lot of farmers will let you hunt on their land too bc hogs destroy their crops.
PS: Don't bother shopping at Alabama outdoors. Nothing but an overpriced uniform shop for frat boys and their boomer parents.