No matter where a package is going, there's no difference if it's to Alaska or Hawaii, it's still part of the United States.
A) parcel post - doesn't matter the distance as much as the size of the box. There's a slight balloon charge for any box over 12".
B) media mail - any kind of media, books, CD's, and the such qualify. It's cheaper than parcel, but subject to inspection. If you mark it as media and it isn't, you're responsible for the price difference before it's delivered.
C) priority mail - There's zones set up across the US, the greater the difference in zone numbers, the higher the price. There's also a significant surcharge in any package over 12".
D) priority flat rate - same price no matter the distance or weight.
E) priority same zone flat rate - these are medium and large priority flat rate boxes for anything being shipped within the same zone number (it's about half the cost of regular flat rate priority).
Every price is based on weight. More the weight, more the price.
Sorry... didn't read the part about it being a remote site in Alaska... that probably changes things.