The deal with a .22 rifle is that almost any El Cheapo .22 will let you do a lot of practice for very little money. Doesn't matter whether it's a bolt action or a semi-auto, except that the bolt action forces more discipline so you don't just go bang, bang, bang for the fun of it with no learning process.
Practice from the offhand position, as well as leaning against a tree or sitting or kneeling. All stuff that you'd expect out in the boonies.
For a hunting rifle: It's hard to find a rifle that won't shoot accurately. The most important point is that the rifle fits your body comfortably. Go to some fairly large gun store and feel and fondle until you find something that fits. Then get one in one of the calibers metioned above.
I've hunted in the Appalachicola River bottom "jungle", and most shots are under 100 yards. I don't know if wild hogs are in your ideas, but I'd suggest a .308 over the .243 if that's the case. (I've killed a good many deer with a .243.)
I prefer scope sights. For the relatively close-in shots you're likely to take, any fixed-power 4x of reasonable quality will do just fine. Just avoid any super-cheap "deals". (I've killed deer to 350 yards with 3X.)
Nuff fer now,
Art