Traveling by Airplane to Alaska is definitely the fastest and probably the cheapest way to arrive here. Short on Vacation time definitely fly. Map out what you want to see ahead of time.
My favorite airlines is Alaska Airlines.
Anchorage is home to the Ted Stevens International airport which is the main hub in and out of Alaska. Alaska has several smaller commuter type airplanes which service the outlying communities.
You can fly into Fairbanks or Juneau, but you would probably just end up stopping in Anchorage anyway, so why not start there.

Here is a list of the domestic airplanes that service Alaska:
Alaska Airlines
American Airlines
Blue Jet
Sun Country
U.S. Airways

Domestic or international flights can be booked at Priceline. Don’t like their price give them a bid. I once bid $40 for a 5-star hotel in Miami and won. It was fantastic! I have hints on the hotel page to get you the cheapest hotels on Priceline so check it out.