Our plan was to make his mortgage payments for several years while we rent the place out, in which time the house value would appreciate while the mortgage balance would decrease, creating room for profit in the end.The value of the property at the time was about $105,000 and he owed $101,500.

Hello BP community,I am putting together a proposal for a rental property investment for a foreign national with 2 proposed financing options:30% down payment, the remaining balance financed or Cash purchase.Per my market research in this area, the projected gross income will be72K.

What is the best balance of cost and looks?

It might be a more balanced 4-6%.This isn't exactly what you're asking , but I just read the winter 2018 Fannie Mae report on multi-units in Denver (i.e.: apartment rentals).

For example, if I sold 1/2 the balance of the note, the yield DOUBLES to ~20% on a 10% face rate note for the note buyer (unless of course I'm the note buyer, then it's okay :-)Pardon my french, but I will be a son of a b*tch before I pay a totally passive note investor that rate of return in this low interest rate enviroment. 

I have a homeowner who has little to no equity in a property in the Memphis area ..the home can rent for 600$ More than the original loan monthly mortgage amount .. the arv is 175,000 the balance left  on the home is 152,000 ..

You will still have to come up with the full down payment, but the combination of the original DP added to the monthly payments should reduce the balance due at the time of the balloon payment to the point where 20% of that should be even less than the balance of a DP if you could get credit for the original payment the way you wanted.

Once I scale up, how do I balance between getting approved and not hurting my credit score too much?

Lenders will look at your balance sheet, normally requiring a personal financial statement which includes all of your assets and liabilities.

Find the balance between a good market and the number of existing STRs as well as the barrier to new entrants in that market.