Butte's median home price sits at $225,000, 46% below the $420,000 national median. On a $52,000 median household income, that puts the price-to-income ratio at 4.3x, or 4.3 years of gross pay for the purchase price alone.
Butte's 0.82% property tax rate runs below the 1.1% national average. That's $154/month on the median home here, not a rounding error against the mortgage payment.
Montana levies a state income tax on top of the $1,420/month this mortgage runs. Model your real after-tax take-home before deciding how much payment you can carry.
Butte's cost of living index is 86, below the 100 national baseline. That's on top of the housing numbers above, not instead of them.
Butte's median home price runs 41% lower than nearby Billings: $380,000 there versus $225,000 here.