Several rules you will need to abide by;
You must have a guide for Grizzly/Brown Bear, Sheep and Goat until you have lived in Alaska for 12 consecutive months.
In certain areas of Southeast Alaska, you'll need a special permit to hunt black bear without a guide under "non-resident status". Check the regulations or stop by ADF&G office at 333 Raspberry Road in Anchorage for info, 907-267-2257 hunting line.
With your PCS paperwork you can get a "non-resident military license" but will have to show your PCS papers to get the "resident rate". You may qualify for a free license if active duty and you can get the application at Alaska Hunting and Trapping Information, Alaska Department of Fish and Game
You wont find a guided sheep or goat hunt in Alaska for less $7,500.00 per person, wont find a grizzly/brown bear hunt under $9,000.00 per person, and those rates wont include your airfare to/from the guide camp or other transportation, big game tags, etc.
Your best bet as of now is stick to species which require no guides and are relatively inexpensive hunts; Moose, Caribou,Sitka Black tail Deer, Black Bear in most areas.
If you have the fever to hunt and the coin to drop on a guide, research them through ADF&G and some of the local forums, Outdoors Directory
is a good Alaska based forum with a few serious hunters on there and a lot of guys full of B/S and hot air. Read wisely and you can sort through all the B/S.
If you have questions and info on hunts you can participate in without a guide drop a PM.