My understanding of human nature tells me that most of these schools are there primarily for the monetary profitability (which is not to say they can't be good schools, but I bet that's not the primary reason they exist).

Institutional lenders will not give a first timer 100% financing, you could bring on an equity partner into the deal which would be your best bet. 

From the down payment alone what's you best bet, $125k property somewhere using 20% down loan. 

I personally (and professionally) think looking inside of 465 is a great bet!

Silly question here but just to confirm.....if you transfer a property from your name to an LLC does the LLC become the new borrower on the mortgage or does it stay in the individuals name?

Quote from @JD Martin: Quote from @Lauren Kormylo: I bet that the majority of their guests use their phones to book anyway.

In a sub2 the loan stays in the sellers name, in an assumption the loan is changed to the buyers name.

Quote from @Bruce Woodruff: If the monthly NET profit is truly -$100 (I would bet that it's actually less than that), then I would sell and move on.

and this sounds like my best bet for building sweat equity at my price point.  

Best bet would be going to a local community bank or credit union.Whats the reasoning for a HELOC?