Well, it turns out the entirety of my physical life can fit in nine boxes, two check bags, and one carry-on backpack. Tickets from Portland to Anchorage to Bethel cost around $350. Shipping my boxes to Kipnuk through USPS came in around $260. All told, it was a lot less than I expected. Also, the LKSD (Lower Kuskokwim School District) reimburses new teachers up to $1,000 for shipping and travel expenses.
Stuff I shipped:
Candy, Food, Kitchen Stuff, Some Clothes, Bathroom Stuff, Survival Gear, Movies, Books.
Stuff I'm flying with:
Computer, Hard Drives, Cameras, My Bear 'Brownie', My Pillow 'Pillow', Chocolate, Clothes, First Aid and Emergency, iPod, Star Wars Comics, a copy of The Call of the Wild and White Fang.
A lot of people have recommended traveling light and ordering other stuff once you get out to the village. Apparently, some teachers end up leaving a lot of housewares behind, and the locals will help you decide what else you need to order. I basically shipped and packed enough to get me through the first few weeks out there.