Not all doom and gloom ,if you are leaving the service that means you have vet points in the federal system and there are a lot of federal jobs in the state. If your retiring then you have a few years on you, and while it sucks getting old most places give some form of property tax relief for those over 65, and those over 60 receive a Permanent ID card that acts as a hunting ,fishing ,trapping license.
Fishing here can be the best and there is a lot to choose from, but there again most has cost involved, the best is usually as far off road as you can get, even salt water fishing gets better with a little distance, so your going to want a boat, or a friend that has a boat, if your that lucky, treat that friend well, remember he's got a lot invested. Unless your into ice fishing , fishing season is short and very busy, you can do a lot of running no matter the part of the state you choose, salmon runs vary from year to year, and river to river, Kings in late May to silvers in Sept. Oct. Pike year around Burbot tru the ice, Grayling as soon as you can find open water, and more.
Moose hunting is still open in lots of places to everyone[Till fish & game gets their way] but there are not a lot of legal moose,and there is a lot of places to look. There are lots of black bears, and some days way to many grizz, sheep hunting seems destined to go to a drawing system for the whole state, and most places goat hunts already are.Deer hunting here is restricted to the extreme coastal areas and islands. Caribou are found across the states larger areas [none in the south east, or panhandle] in herds that number from a few hundred to many thousands, but most are either very restricted or very hard to access.
One more doom and gloom, the economy here is usually about two years behind that of the lower 48 and does appear to slowing by a large factor this year [about two years behind] .
No one can answer the questions you and your family will have but you, a trip here will give you a brief look at Alaska , but only by making the move can you answer the questions. My family and moved here in April 87, for a one year trial, we found our home and have never even given a move outside a serious thought, When we leave here we really will be in Heaven, till then Alaskans as close as we've found.
Alex