If hunting and solitude are high priorities for you then Anchorage probably isn't the ideal place to be. Bear in mind that approximately half the population of Alaska lives in Anchorage and the adjacent areas of the Mat-Su. I lived in Anchorage for about a year when I first moved to AK and I couldn't get out of there fast enough. There was just too much traffic and noise and not near enough of Alaska for my taste. I moved to Fairbanks, have been there ever since, and have no intention of ever going back to Anchorage. Anchorage is closer to some of the prime fishing destinations, namely the Kenai, but that river is a frickin' zoo during the prime salmon runs. Hunting is far better in the interior, and there's plenty of good fishing within a reasonable driving distance. All that said, your best bet is to look for the area that will provide you the best opportunity for decent employment. Hunting in Alaska is generally time consuming and expensive so if your job doesn't provide the funds and the free time you're pretty much out of luck regardless of where you live.
aaalaska hit it on the head regarding hunting and the densities of animals up here. Most people think Alaska is like what they've seen on the Discovery Channel and there's huge herds of caribou and moose all over. In reality overall densities of game animals are extremely low up here. Sure you might find yourself in a massive herd of caribou, but they range so far and wide that more often than not that isn't the case. Areas up here that have high moose densities usually have fewer than 2 moose per square mile, so they're usually very few and far between.
Moving to Alaska is a huge commitment. If you've never been here I'd recommend you make a trip up and at least travel around the primary population centers and see what suits you best. You might decide that southern bbq, whitetail deer, turkeys, and largemouth bass in Tennesse aren't all that bad after all.
AK Jeff