working with the investors that I do they find that the financing options with new construction are fare better that most resale homes.  

Rentals create cash flow, and that's what we want as real estate investors, but you need cash on hand for unforeseen circumstances.The AC needs to be replaced, that's $7K to $10K or more depending on the size of the house and if you have one rental, it will eat all your cash flow, same to replace a roof, etc, or if tenant trash the home, you need money to fix it again.To me personally a nice rental portfolio that is healthy consists about 10 units, so if you have an issue with a house the portfolio can cover the repairs and still healthy, but when starting you need to have cash on hand just in caseYes, there are multiple strategies you can use to hack your way to buy your first rental with minimum cash, but I would start wholesaling or fix and flip a few deals to create that cash as fast as possible

Last July I purchased a home from HOA foreclosure auction.

Any pro tips you can share as far as vetting tenants or collecting rent? 

I have thought about buying a four plex and claiming one of the units will be my home to take advantage of a lower down-payment.

Quote from @Stephen Homes: She's violated the lease and damaged the property, so you can legally terminate it.

I've noticed there are many homes for sale from large construction companies in North Fortworth, but not as many in the  areas like Euless, Hurst, and Bedford.

I just find it so strange that I had 3 evictions out of the 3 homes I own.

After the tenant moves into your home, things become your responsibility.As a more immediate remedy, try to do away with those trial leases.

:Hypothetically speaking - let's say someone replaced the countertops in their primary home at the same time they were rehabbing a rental property.