Keep in mind that you need to live in Montana six months to establish residency, which is required to purchase a hunting licence. (make sure you bring an archery tag or license from your state if you have not completed a bowhunter ed course). Also the elk / deer special hunt application deadline is March 15th. That means you need to move here by mid-September if you want to participate in the drawing.
If I had the choice between Billings, where I now live, or Helena I would have picked Helena. But at least I'm in Montana. My advice would be to go for it.