These typically are properties with finished basements and separate entrances.

So as soon as the renters in the basement left for work I started ripping up my carpet in the entrance of the house so I could replace it with some nice porcelain tile.

Wonder,  if that one entrance way board of the framing isnt loose too.

The basement is divided into a mother-in-law apartment with a private entrance.

It has a private entrance, full bath, and a full kitchen with a tiny home/industrial concept.

We have found the following benefits:1) We can demand an extra $30 - $50 per month in rent for the convenience of en-sute laundry;2) Tenants pay their own electricity, hot water and, if sub-metered, water costs related to laundry;2) In small residential buildings (like your quad) we often no longer require an electrical entrance for the house;3) Vandalism of the laundry machines is non existent {though it was never significant} ... if something happens to a machine, we know who is responsible.4) High-efficiency residential laundry units are 50-70% the capital cost of equivalently performing commercial coin-op machines  {between the extra rent and depreciation, we find the machines are paid-off in ~2.0 - 2.5 years}.

Like you, I too have been lurking to help guide best entrance into REI.

Because multi units are so uncommon around here it may be easier to purchase a home with a basement, in-law suite or garage with a separate entrance that you could convert into a rental unit.  

Question - if the upstairs unit has only one entrance, can I do FHA on it?

I have those in the entrance way--so high traffic--of two of my buildings.