I think your approach is reasonable - you know what your goals are, you're starting with the ones most important, then determining what your options are within that.

One way to put numbers onto your goal-based approach is determine what percentage of savings you need (25%, you said), then multiply your income by that (obviously the income you expect after moving), then subtract other expenses. That would give you the annual amount you can spend on housing. Don't forget your repairs and capex (capital expenditure, meaning periodic replacement of everything major).

Example: Suppose you earn 60k, then you need 15k savings rate. Suppose other expenses are 20k (but use your real numbers for this, and include any allowances in case of higher living cost after your move). 60 less 15 = 45, 45 less 20k = 25k, that's your max for total housing. Perhaps you will conclude 18k for annual principal, interest, insurance and taxes; determine insurance and tax rates in the new area are 50% of principal and interest (again, please research real numbers, 50% is my example); therefore 12k of principal and interest. Then determine expected interest rate (could go up in 2 years, per the Fed). Then calculate from that, using a 15 year note to own the home at age 50, what down payment and mortgage would fit the 12,000 per year in your max affordable budget.

I don't know your numbers for all these variables, but I would use 5% interest to be safe (accounts for 2% increase in next couple of years; may or may not happen). Anyway, have fun exploring, and I hope all of your plans bear fruit.