In Utah County the cheapest “House” for sale is 600 square feet, 2 bed, 1 bath, at $300k.
So at current interest rate it would be $1,800 a month mortgage(assuming you put the 60k down payment! A decent amount more if you do 3% down.)
The cheapest condo/town in utah valley is 205k, 1,100 square feet, on a 400 square foot lot. But due to a $500 HOA fee the monthly cost is still 1,700 a month (assuming 20% down).
With 3.5% down they’d both be closer to 2.1k +PIMI.
So yeah, how is where you live doing?
The OP said “house”. Interpret that however you’d like I guess. If you bought this place for $10k in cash, I don’t know who exactly would stop you from clearing out a room and living in it while working on it.
You can get a loan for just about anything from the bank. You don’t even have to be very specific about what you’re using it for. All they care about is credit history, what interest rates they’re giving you, length of loan, blahblahblah