Brushstomper:
I live in Bozeman. It is the most overcrowded, hippie hangout in the west. I wouldn't move here if I were you. It will be a waste of your time and effort. The nearest hunting is at least 200 miles from here. All the elk were eaten by the wolves and the birds have all come down with the Shanghai Chicken Flu.
OK, so I probably didn't scare you off. There is good hunting here. It is probably somewhat overrated, but can be good if you work hard at it. There is adequate public land, but that requires horses or being in really good shape to be continually successful. We all get lucky occasionally and find a stupid elk within a mile of the trailhead, but not very often.
The private lands are all leased or require tresspass fees. If you are a bird hunter, you will pay money to hunt birds in this valley. If you are willing to travel, you can find decent bird hunting in Eastern Montana.
Guys who have lived here for a while had to work extremely hard to find their honey holes or to make landowner connections. Do not expect them to tell you much, myself included.
If you don't need to make your living here, it can be good. If you have to work for a living, prepare yourself for wages below the national average and housing costs more than 120% of the national average. It is a hard gap to cover. A lot of folks come here to follow a dream, only to have the economic realities of this place shatter the dream.
Good luck if you move here. If you want to get connected to the hunting crowd, there are three groups to look up. Join either the RMEF or DU committees, or join the Headwaters Fish and Game Association. The hardest core hunters in the valley belong to those groups, and some of the really hard core guys belong to no groups at all, not wanting to get pressured to share their knowledge.
Good luck!