Are you familiar with why a lease to own contract may not be a great option? And they are extremely rare in a seller market like this.
Owner financing is rare as well because most people don't have equity, and if they do, they need that to apply to their next home purchase. You are either buying a foreclosure, short sale or a standard 'flip' sale from an investor who wants his money back ASAP.
$20K is not enough for private financing....you need at least 30% down payment.
I suggest you wait out the three year's before you can qualify for FHA financing and find a good rental.