MisplacedHog, in your shoes, what I'd be doing is applying as widely as you can, to as many nuke plants as you can. Everything else - being selective about type of reactor, location of plant, and so on - is mainly going to be the concern of folks with a few years' experience and several offers on the table. Your goal at this point is simply to get your foot in the door of this industry. If anything, you should be selective with respect to factors that make a plant less "desirable" but more likely to consider you (unglamorous location, etc).
You can still get hired in this industry with no nuclear experience. But you're going to have to work for it. The days of cherry-picking a plant and saying "This is where I'm getting a job" are long gone - if they ever happened at all. If you want to work at ANO, you're going to have to either already be local to the plant or, more likely for you, get some nuke experience under your belt elsewhere first. (And who knows? Like many nukes, you may find that the 'elsewhere' is a lot better than you thought)
Now... if returning to Arkansas is more important to you than working in nuclear power, per se? Then I'd be considering a different kind of career change, perhaps to a fossil plant or other industrial facility in the state. You have to arrange your priorities first before you can decide how to proceed.