Start with the fact that the odds are against getting an unsecured loan for a purchase as big as a house. Second, unsecured loans have higher interest rates then do mortgages, so even if you could find an unsecured loan, you would be paying even more in interest than on a mortgage.
This leaves cash for the house (no interest) or shorter mortgages (higher payments, but more goes toward the principle, thus reducing interest).
As for the part-rent, part buy (rent-to-own), you would most likely still be paying for 90-95% of the house after a;ll is said and done. Only a portion of the rent goes into an escrow account (For example, let's say you were going to rent to own a $100,000 house - if you paid $1400 in rent, probably $400 a month would go into escrow, which means at the end of the year, you would have $4800 to put toward the house - only about 5% of the purchase price).