The last two times I bought a house, I started with a soft limit and a hard limit on my mortgage payment. The soft limit is how much I intend to pay, the hard limit is the amount I will not go over, no matter what. Both amounts will be less than the max I can absolutely afford.

From there, my approach is to look at the numbers for a 30-year and a 15-year mortgage. Once I get those, I use an amortization calculator to see what happens when I overpay. If the payment amount is lower than the soft limit, I use that as the actual amount I pay. If the payment is between the two limits, I assume I pay the hard limit. Then I choose the mortgage that has me paying the least amount of interest over the lifetime of the loan. The mortgage on our last house was a 15 year and we had it paid off in 9 without stressing our budget.