Here's the website for the Ouachita National Forest:
http://www.fs.fed.us/r8/ouachita/
On the right side of this page is a list of trails. I think you should start with the "Short Walking and Enterpretive Trails," move up step-by step as you build confidence and skills to the "One to Five Miles Hikes," off-trail exploring, and perhaps through-hiking the 190-mile Ouachita Trail eventually.
http://www.fs.fed.us/r8/ouachita/recreation/trails.shtml
Forget the axes, "hacking" tools, and hunting knives (unless you're hunting, of course) for hiking and backpacking in Arkansas. You'll just need a simple pocketknife as described in the Ten Essentials list, perhaps a multi-tool, SAK, or whatever you already own.
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Keep in mind that the Ouachita National Forest is public land, owned by all Americans equally. Keep it clean for the next person by following a no-trace ethic. Here's the best summary I've seen, combined into a simple common-sense list:
http://www.lnt.org/programs/lnt7/index.html
I dissagree about their item, "pack out toilet paper" though. At least in Arkansas it's not necessary. Just bury it with the turds and it should be fine. There's a good reference book,
How to Shit in the Woods that gives more details and why packing out TP is necessary in some environments.
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Here are some hazards you might encounter in Arkansas. It would be in your best interest to read a bit about managing the risks and what to do in any of these events:
1) flash floods - it seems someone dies each year in Ark trying to cross swollen creeks.
2) insects and deseases - ticks, mosquitoes, gnats, flies, scorpions
3) poisonous snakes - rattlesnakes, copperheads, cottonmouths
4) bears - more for their protection than your's, "A fed bear is a dead bear"
5) poisonous and irritating plants - nettle, poison ivy, briars
6) two-legged irritants - camp far enough away that you aren't visible from trails or roads
7) seasonal weather extremes - dry periods, floods, extreme heat, winter storms, etc.
-Bob