Apartment hunting is the pits. I have to say, after spending the night sweating to death in my over-priced, un-air conditioned apartment last night that I am not good at finding places to live. My friends had great apartments, with fireplaces (not working ones, but even a decorative fireplace is nice), and hardwood floors, and sun rooms, and patios, and they didn’t pay much more rent than me, but I don’t know how to find that kind of place.
I’ve been trying to think of qualities to look for in an apartment to help me with my search. It needs to allow pets, and even though I don’t know when I’ll be getting a dog, it has to allow for both cats and dogs, just in case. I’d really like a place where I could line-dry my laundry (this might not happen, but it makes sheets smell so good! I’ve been drying stuff out on my fire escape, but I feel like that evokes the morning after a wedding night in medieval times, and that’s kinda gross. Also, sometimes things blow away and fall into the parking lot behind my building, which defeats the purpose of washing them in the first place), and for that matter, I’d like a place that comes with a washer and dryer so I don’t have to obsess over quarters. I’d like a fireplace (fortunately, they seem to be pretty common in Alaska- even the less-nice places I’ve seen at least have the gas ones), and a decent-sized kitchen. I think those are all reasonable qualities to look for, but I don’t know how to find that kind of place.
Turn Towards the Sun 
If I were you, I would not try to find a long-term home from a distance. Moving is, of course, the worst, but think about finding a liveable, affordable place for your first year and then looking for something better once you’re there. After you’ve been on the scene for a bit, you will know people, and you’ll be able to scout around for places that don’t get posted on the websites. And moving in-town is always easier than moving cross-country, especially since I assume everyone you know at that point will own a huge truck.
Research the neighborhoods, I guess, and then go from there, relative to where work is and transport options. When I moved here I worked far(ish) from home, but transport was convenient and accessible between the two, which made a difference. Close to work is convenient, if work is in a place where the rest of what makes living there easy, like food shopping, but otherwise go for the transport options first and worry about commuting later.
Lots of craigslist, not much else, looks like, but here’s a small one that likes dogs: http://anchorage.craigslist.org/apa/3915533627.html
Emily’s point about just finding something for a reasonable period and then expanding your search once you know people and the lay of the land, go for more. Greg’s point about convenience of commute and places to shop when your time will be limited makes sense, too. Keeping in mind the hot, tiny, narrow little place you endured (after the first really bad place), should give you confidence that you can endure until the ideal comes along.
Perhaps there is a bear equivalent to Craigslist. Rupert’s List?